Representation Learning for Maritime Vessel Behaviour: A Three-Stage Pipeline for Robust Trajectory Embeddings

Abstract

The growing complexity of maritime navigation creates safety challenges that drive the shift toward autonomous systems. Maritime vessel behaviour modelling is critical for safe and efficient autonomous operations. Representation learning offers a systematic approach to learn feature embeddings encoding vessel behaviour for improved situational awareness and decision-making. We introduce a three-stage representation learning pipeline evaluating six architectures on real-world AIS trajectories. Grouped Masked Autoencoder (GMAE)-Risk Extrapolation (REx) combines group-wise masked autoencoding at the semantic feature level with risk extrapolation regularisation, forcing encoders to learn cross-group dependencies between temporal, kinematic, spatial, and interaction features. DAE and EAE provide robust and uncertainty-aware baselines. Evaluation uses a dual-pipeline framework on two years of Kiel Fjord AIS data (176,787 trajectories, 527,225 segments). Pipeline 1 applies three-stage representation learning using vessel-type classification as encoder selection probe. GMAE-REx achieves 86.03% validation accuracy, outperforming DAE (85.63%), EAE (85.56%), and baselines Transformer (84.93%), TCN (76.27%), LiST (85.12%). Pipeline 2 applies unsupervised clustering to discover intrinsic behavioural structure. Learnt representations consistently outperform expert features on DBCV, conductance, and modularity metrics, organising trajectories by operational context rather than vessel type. This behaviour-oriented organisation enables cross-vessel knowledge transfer for autonomous navigation, VTS monitoring, and safety analysis.

1. Introduction

Maritime transportation remains the backbone of global commerce, facilitating over 80% of international trade by volume and handling approximately 12.6 billion tonnes of cargo in 2024 [1]. The Automatic Identification System (AIS), mandated by the International Maritime Organisation (IMO) under the International Convention for the Safety of Life at Sea (SOLAS), has transformed maritime domain awareness by providing real-time vessel tracking data at an unprecedented scale [2]. Modern maritime stakeholders, including port authorities, vessel traffic services, and autonomous navigation systems, now have access to millions of AIS messages daily, creating rich spatio-temporal datasets that capture the complex dynamics of vessel movements across diverse operational contexts. The large-scale availability of trajectory data presents a compelling opportunity for understanding maritime behaviour at scale through Machine Learning (ML) approaches that could enhance Situational Awareness (SA), improve safety, and support the emerging paradigm of Automatic Maritime Operations (AMO) [3].

However, the operationalisation of data-driven maritime intelligence remains largely unfulfilled.

Despite the availability of vast unlabelled AIS data, most existing approaches rely on supervised learning paradigms that require extensive manual annotation of vessel behaviours—a process that is expensive, subjective, and inherently limited in scope [4,5].

Moreover, the maritime domain exhibits pronounced environmental heterogeneity: vessel behaviours manifest differently across varying traffic densities, geographical contexts, and temporal conditions. A cargo vessel approaching a busy port navigates fundamentally different conditions than the same vessel transiting open ocean, yet both represent instances of the same underlying navigational objective.

This environmental variation creates substantial challenges for learning representations that generalise beyond the specific conditions encountered during training.

The analysis of maritime trajectory data presents several fundamental challenges that limit the effectiveness of existing solutions. First, environmental heterogeneity and domain shift pose significant obstacles: representations learnt from one operational context—a particular port, traffic regime, or season—may fail to transfer to others, as standard learning methods implicitly assume that training and deployment conditions are drawn from the same distribution [6,7]. Second, unlike domains with homogeneous feature semantics such as pixel grids in computer vision, AIS-derived features exhibit semantic complexity. Temporal features encode when observations occur; kinematic features describe instantaneous motion state; spatial features characterise spatial context; density features quantify traffic conditions; and interaction features capture relationships with nearby vessels.

However, raw AIS broadcasts inherently lack this semantic categorisation, transmitting only basic navigational parameters, including position, speed, course, and heading, without distinguishing their functional roles in behavioural representation. This absence of structural organisation conceals the causal dependencies between feature categories—for instance, how temporal context and traffic density jointly influence kinematic decisions, or how interaction features emerge from the interplay of spatial positioning and relative motion. Consequently, ML models operating on unstructured feature sets may exploit superficial within-category correlations (such as temporal autocorrelation in speed measurements) without discovering the deeper cross-category relationships that characterise coherent navigational strategies [8]. Third, expert annotation of vessel behaviours is expensive, time-consuming, and inherently subjective [9]. The resulting label scarcity limits the applicability of supervised approaches and motivates unsupervised or self-supervised methods that can learn from large-scale unlabelled data.

The transition towards Maritime Autonomous Surface Ships (MASS) amplifies the urgency of developing robust behavioural representations. Autonomous navigation systems must operate reliably across diverse maritime environments, recognising normal navigational patterns, detecting anomalies, and making safe decisions even in conditions not explicitly covered by training data [10]. The European Maritime Safety Agency (EMSA) reported 2590 maritime incidents in 2023, with over 65% attributed to human decision failures related to inadequate SA [11].

While MASS promise to mitigate human error, realising this potential demands representations that remain valid across the distributional shifts between training environments and deployment scenarios—a challenge that conventional supervised learning approaches fail to address [12]. Furthermore, safety-critical maritime decision-making requires not only accurate predictions but also reliable quantification of prediction confidence, enabling autonomous systems to recognise when they encounter unfamiliar conditions and defer to human operators or adopt conservative strategies [13]. Current trajectory analysis methods lack principled mechanisms for distinguishing between uncertainty arising from inherent environmental stochasticity (aleatoric) and uncertainty stemming from insufficient training coverage (epistemic), limiting their applicability in safety-critical autonomous navigation; see [13].

This article addresses the fundamental challenge of learning robust behavioural representations from maritime AIS trajectory data that generalise across diverse environmental conditions. We propose a comprehensive three-stage representation learning pipeline that combines self-supervised pretraining with domain generalisation techniques to address the unique challenges of spatio-temporal maritime data. GMAE-REx (Group-wise Masked Autoencoder (MAE) with REx) combines structured masking at the semantic feature-group level with REx regularisation that penalises reconstruction strategies favouring particular environmental conditions, encouraging representations that work equally well across traffic densities and geographical contexts. We complement this novel architecture with a Denoising Autoencoder (DAE) that provides a strong baseline through reconstruction of noise-corrupted inputs [14] and an Evidential Autoencoder (EAE) that extends the denoising framework with principled uncertainty quantification through evidential regression, enabling distinction between epistemic and aleatoric uncertainties essential for safety-critical applications [13].

We evaluate learnt representations through two complementary experimental pipelines that together provide comprehensive assessment of representation quality. The first pipeline employs supervised classification using vessel type as the prediction target, with linear probing on frozen encoder representations to isolate representation quality from fine-tuning effects. This pipeline explicitly assesses robustness across environmental conditions through per-environment metrics, worst-group accuracy, and accuracy variance across traffic density quartiles. The second pipeline applies four unsupervised clustering methods (Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN), kNN-Leiden, Variational Bayesian Gaussian Mixture Model (VBGMM), First Integer Neighbour Clustering Hierarchy (FINCH)) with intrinsic structure quality metrics (DBCV, conductance, modularity) to assess whether representations naturally organise trajectories into coherent behavioural groups aligned with operational context without explicit supervision.

This work contributes several novel insights to the field of maritime trajectory representation learning:

(i)

Comprehensive Processing Pipeline: We present an extensive AIS data processing pipeline that transforms raw positional broadcasts into richly annotated trajectory representations. This includes ship-level features (e.g., kinematic states, temporal encodings, vessel characteristics), ship-to-ship interaction features (e.g., Time to Closest Point of Approach (TCPA), Distance at Closest Point of Approach (DCPA), relative bearing, collision risk indicators), and ship-to-environment features (e.g., water depth from nautical charts, distance to land, proximity to restricted areas, traffic density estimates). The exhaustive nature of this feature engineering process, necessitated by the sparse and noisy characteristics of AIS data, represents a significant methodological contribution that enables downstream representation learning.

(ii)

Three-Stage Representation Learning Framework: We propose a systematic pipeline comprising self-supervised pretraining, linear probe evaluation, and full fine-tuning reference, with hyperparameter optimisation conducted exclusively on self-supervised validation loss to prevent information leakage from downstream tasks.

(iii)

Environment-Aware Self-Supervised Learning: We adapt REx from the domain generalisation literature to maritime trajectory representation learning, demonstrating its effectiveness for learning representations that generalise across traffic densities and geographical contexts.

(iv)

Semantic Feature Grouping: We introduce group-wise masking strategies that respect the semantic structure of AIS-derived features (temporal, kinematic, spatial, density, interaction), forcing models to learn cross-category relationships rather than exploiting within-category correlations.

(v)

Uncertainty-Aware Representations: We integrate evidential learning into the autoencoder framework, providing principled estimates of both epistemic and aleatoric uncertainty essential for safety-critical maritime applications.

(vi)

Comprehensive Dual-Pipeline Evaluation: We establish an evaluation methodology combining supervised linear probing for encoder selection and unsupervised clustering with intrinsic quality metrics (HDBSCAN, kNN-Leiden, VBGMM, FINCH) to assess both discriminative capacity and natural behavioural structure discovery.

(vii)

Reusable and Adaptable Framework: We present a modular representation learning framework that generalises across maritime geographical regions and downstream tasks 1. The three-stage pipeline can be deployed to different operational contexts by adapting the data processing module to local AIS sources and replacing the probing head (e.g., from vessel-type classification to collision risk regression) whilst preserving the self-supervised pretraining strategy. This design enables transfer learning for region-specific behaviour modelling and task-specific embedding optimisation without requiring large-scale labelled datasets.

The remainder of this article is organised as follows. Section 2 reviews related work in maritime trajectory analysis, self-supervised representation learning, and uncertainty quantification. Section 3 presents the comprehensive AIS data processing pipeline, including data sources, standardisation, trajectory extraction, feature engineering, and collision risk computation. Section 4 details the representation learning models, including the unified encoder–decoder architecture, and the specific implementations of GMAE-REx, DAE, EAE, and baseline architectures (Transformer, Temporal Convolutional Network (TCN), Linear Spatial–Temporal Feature Extractor (LiST)). Section 5 describes the dual-pipeline evaluation framework, experimental protocols, and performance metrics. Section 6 presents the experimental setup, dataset characteristics, and reports results for both supervised encoder selection (Experiment I) and unsupervised structural analysis (Experiment II). Section 7 discusses and interprets experimental results across both representation learning pipelines, analyses practical implications, and outlines study limitations. Finally, Section 8 summarises key findings and outlines directions for future research.

2. Background

Maritime transportation operates in a complex, dynamic, and inherently hazardous environment. IMO classifies maritime operations as safety-critical systems where failures can result in loss of life, environmental catastrophes, and significant economic damage [15]. EMSA reported over 2500 maritime incidents annually, with human error accounting for the majority of accidents [11]. These challenges motivate the development of advanced decision-support systems and autonomous capabilities to enhance maritime safety and operational efficiency.

The last decade has witnessed strong efforts towards autonomous vessel navigation. Currently, existing technical studies and prototypical solutions for autonomous and semi-autonomous behaviour are primarily confined to standard assistance systems, such as open-sea autopilot, or focused on short-distance cargo transportation within coastal areas [16].

2.1. Situational Awareness

Situational awareness (SA) is a fundamental concept in autonomous systems, referring to the perception of environmental elements and events, comprehension of their meaning, and projection of their future status [17]. In the context of autonomous maritime navigation, SA encompasses the vessel’s ability to accurately detect and track surrounding entities, understand the maritime traffic situation and environmental conditions, and anticipate potential hazards or conflicts. Achieving robust SA is critical for safe and efficient autonomous vessel operation, as it forms the foundation for informed decision-making and collision avoidance.

Autonomous surface vessel navigation behaviour is based on continuous observation and assessment of the current environmental conditions—which is then turned into concrete navigation actions by an autonomous controller (e.g., [18]). Consequently, situational awareness is a prerequisite for autonomous navigation.

Situational awareness frameworks have been extensively studied across safety-critical domains, including aviation [17], nuclear power operations, and military command and control systems. These frameworks emphasise hierarchical perception, comprehension, and projection capabilities that are equally relevant to maritime autonomous systems.

In the last decade, various contributions have considered aspects of situational modelling and awareness problems, including approaches to reconstruct ship trajectories from spatio-temporal historical data [19], modelling of ship trajectories in safety-critical conditions—such as collision avoidance manoeuvres—using optimisation heuristics [20], a prediction of trajectories for the own and other ships in the vicinity based on ML technologies such as artificial neural networks [21], modelling of current constellations based on observational data [22], or an analysis of ship trajectories [23]. However, there is no unified approach for maritime navigational situation modelling and analysis yet established, which is partly driven by the high heterogeneity of available input data.

2.2. AIS for SA

The various maritime test environments oriented towards autonomous navigation (i.e., prototype test ships for experimentation purposes such as the “MS Wavelab” in Kiel, Germany [24]) have different sensor constellations, characteristics, and capabilities. The only reference data common in all use cases are AIS, which is an integral component in today’s maritime navigation and safety. The AIS is an automatic tracking system used on ships and by Vessel Traffic Services (VTS) for identifying and locating vessels by electronically exchanging data with other nearby ships, VTS stations, and satellites. This system allows real-time tracking of ships, providing vital data that encompass their identity, position, speed, and course, thus aiding vessel operators in collision avoidance strategies [25]. Consequently, the IMO has mandated the adoption of AIS for vessels exceeding a certain size [15,26].

Despite its widespread adoption and critical role in maritime safety, AIS has inherent limitations that impact its effectiveness for SA; it is not without vulnerabilities, including the potential for errors and susceptibility to cyberattacks. These concerns have prompted examinations into the accuracy and integrity of position data transmitted via AIS, as in [27]. Jiang et al. [28] used Monte Carlo simulation to model probabilistic distributions of vessel size, vessel speed, and traffic volume for inland water transport. This research sheds light on the challenges of extracting knowledge from AIS data, which arise from factors such as data volume, incompleteness, noise, and unobserved vessels.

Nevertheless, AIS remains a prevailing choice within the research community for tracking maritime vessels efficiently and cost-effectively [29,30].

In terms of safety, AIS data have been used for traffic management, identifying potentially dangerous locations for maritime transportation, and providing relevant information for traffic control. One of the critical applications of AIS is traffic management, which involves spatial analysis of near collisions to identify potentially hazardous locations in maritime transportation. As an example, Wu et al. [31] investigated vessel conflicts in the Southeast Texas waterway, examining features such as vessel size, spatial distribution, time of day, and collision risk levels using the Vessel Conflict Ranking Operator (VCRO) model. This research identified hotspots with high frequencies of vessel conflicts and evaluated the impact of time of day on conflict density in each hotspot. As an alternative, Yoo et al. [32] estimated near-collision density in coastal areas based on AIS data, pinpointing high collision-risk locations using parameters such as DCPA and TCPA derived from ship location, speed, and course data. Shelmerdine et al. [33] leveraged AIS data to generate vessel tracks and density maps, illustrating temporal variations between months and distinguishing between different vessels around the Shetland Islands. The analysis revealed variations in vessel routes, especially around island groups. As an alternative, Jensen et al. [34] conducted an analysis of cargo traffic outside of San Francisco Bay, identifying dynamic changes in shipping traffic across seasons, both annually and daily. The study highlighted the challenge of documenting shifts in shipping traffic effectively.

As a second major aspect, anomaly and novelty detection (e.g., [13,35,36]) has been performed on AIS data with goals such as the identification of conspicuous ships, the detection of deviation from expected manoeuvres, or an online observation and assessment system. For instance, Chen et al. [37] developed a method to detect and restore anomalies in raw AIS data by exploiting ship maneuverability constraints. The approach classifies abnormal AIS trajectory points based on longitude (lon), latitude (lat), speed, acceleration, and heading information. Anomaly detection criteria include maximum and minimum acceleration thresholds, maximum reachable distance between consecutive points, and maximum angular displacement, all derived from vessel design specifications. The method was validated on 156 AIS messages from a 110 m cruise vessel operating at 10 s transmission intervals near Xiamen International Cruise Center, demonstrating effective identification of drift, acceleration, and turning anomalies. In the context of self-adaptive systems, Goller et al. [38] investigated abnormal behaviour detection in maritime traffic by analysing AIS data from the Kiel Fjord and Kiel Canal region. This approach applies external observation metrics—including configuration stability, configuration coherence, and global parameter usage—to monitor collective vessel behaviour without requiring knowledge of individual navigation strategies. The study demonstrated the effectiveness of these metrics in detecting abnormal events such as the 2022 Kiel Canal bridge collision, where configuration stability exhibited a prominent peak immediately following the incident, providing early indicators for potential re-integration decisions in autonomous navigation systems. More recently, Gao et al. [13] proposed a novel framework named Federated Evidential Learning for Anomaly Detection of Ship Trajectories (FEAST) that advances maritime situational awareness through privacy-preserving and uncertainty-aware anomaly detection. This framework combines federated learning with evidential learning and employs a Transformer-based AutoEncoder architecture to model navigation behaviour from high-dimensional AIS data while explicitly quantifying both epistemic and aleatoric uncertainties. Evaluated on one year of AIS data from the Kiel Fjord, FEAST demonstrated superior performance in detecting out-of-distribution anomalies compared to traditional Variational AutoEncoders, providing interpretable uncertainty estimates that enhance SA for autonomous maritime systems.

Recent work has also applied deep learning directly to vessel trajectory classification. Kim et al. [39] proposed a supervised framework that converts AIS position sequences into trajectory images and fine-tunes a deep Convolutional Neural Network (CNN) initialised from ImageNet weights to classify vessel types, addressing domain shift through transfer learning from a large source domain. This approach demonstrates the effectiveness of convolutional feature extraction for trajectory analysis; it is fully supervised and relies on a labelled training corpus that the authors themselves note may limit generalisation (8679 vessels total).

3. Data Processing and Trajectories Retrieval

The Automatic Identification System (AIS) is a maritime communication and tracking system in which vessels periodically broadcast navigational and identification information via Very High Frequency (VHF) radio to nearby ships and coastal authorities. Introduced by the International Maritime Organisation (IMO) in 2000, AIS was primarily designed to enhance navigational safety and support collision avoidance. Since December 2004, AIS transponders have been mandatory for all vessels subject to the requirements of the International Convention for the Safety of Life at Sea (SOLAS) [2,26].

In recent years, AIS data have been increasingly utilised for a wide range of commercial and research applications, including maritime traffic monitoring, route extraction, and vessel trajectory prediction [40]. However, previous studies have consistently reported the inherently noisy nature of AIS data [41]. This issue occurs particularly in manually entered fields, such as destination and draught, which are frequently incomplete, outdated, or erroneous. Furthermore, transmission errors, irregular reporting intervals, and temporary signal loss contribute to additional degradation of data quality.

To effectively exploit the large volume of available AIS data, we propose a preprocessing pipeline designed to extract, clean, and enrich vessel trajectories. The pipeline follows a modular structure, enabling straightforward adaptation to alternative data sources and facilitating the integration of additional features relevant for downstream analysis and prediction tasks.

AIS transmissions are associated with a Maritime Mobile Service Identity (MMSI) that uniquely identifies each vessel. The messages comprise dynamic information, including vessel position, Speed Over Ground (SOG), and Course Over Ground (COG), as well as static and voyage-related attributes such as ship type, vessel dimensions, and reported destination.

3.1. Data Sources and Decoding

The proposed preprocessing pipeline integrates multiple heterogeneous data sources, including raw and decoded AIS messages as well as geospatial map data, to establish a comprehensive foundation for vessel trajectory prediction and interaction modelling. The selected datasets complement each other with respect to temporal and spatial coverage as well as semantic richness.

• AIS Data Sources

Two independent AIS data sources were utilised to ensure high temporal resolution in the port area while maintaining robust regional coverage.

(i)

Raw AIS Messages (Kiel University of Applied Science)

High-resolution AIS data were provided by Kiel University of Applied Science, see [42], and consist of raw AIS messages encoded according to the NMEA 0183 standard defined by the National Marine Electronics Association [43]. Each message contains metadata describing sentence fragmentation, communication channel, and timestamp information, as well as a payload encoding navigational data. The raw message format preserves the original temporal resolution of AIS broadcasts, enabling fine-grained analysis of vessel motion and short-term dynamics. Spatial coverage is strongest in the immediate vicinity of the Port of Kiel and gradually decreases with increasing distance from shore, particularly beyond approximately 10 nautical miles, as vessels leave the effective reception range of shore-based AIS receivers [44]. The dataset spans the years 2022 and 2023 and contains intermittent temporal gaps caused by receiver outages and adverse environmental conditions.

(ii)

Decoded AIS Data (Danish Maritime Authority)

To complement the raw AIS messages, decoded AIS records provided by the Danish Maritime Authority (DMA) [45] were incorporated. These data are distributed as Comma-Separated Values (CSV) files in which AIS messages are already decoded and represented in tabular form. Although records dating back to March 2006 are available, this study exclusively considers data from 2022 and 2023 to ensure temporal consistency across all data sources. Compared to the raw AIS messages, the decoded records exhibit reduced spatial resolution, as latitude and longitude values are rounded. However, they offer broader geographic coverage, with highest density in Danish waters and extended coverage into the western Baltic Sea, including the Port of Kiel.

• Map and Environmental Data

To enrich AIS trajectories with environmental context, several geospatial datasets were integrated.

(i)

Water Depth (Denmark’s Depth Model)

Bathymetric data were obtained from Denmark’s Depth Model [46], which provides a gridded representation of water depth at a spatial resolution of $50\times 50$ m. The dataset is referenced in the Lambert Conformal Conic projection (EPSG:3034), with depth values defined relative to Mean Sea Level (MSL) according to the Danish Mean Sea Level (DKSML) vertical reference system [46]. The model integrates satellite-derived bathymetry, airborne LiDAR measurements, and crowdsourced depth observations to construct a detailed and high-resolution representation of seabed topography.

(ii)

Water Depth (Hydrographic Survey Data)

Additional bathymetric information was sourced from hydrographic surveys conducted by the Federal Maritime and Hydrographic Agency [47]. This dataset covers the North Sea and Baltic Sea at the same spatial resolution of $50\times 50$ m and is referenced to the Normalhöhennull (NHN) vertical datum within the ETRS89–UTM32 coordinate reference system. The underlying measurements were collected between 1994 and 2010 as part of joint mapping initiatives involving the Leibniz Institute for Baltic Sea Research [48].

(iii)

Land and Maritime Infrastructure Data

Additional maritime context, including coastline geometry [49], restricted navigation areas, and ferry routes, was extracted from OpenStreetMap through the Overpass API [50]. The Port of Kiel is characterised by dense ferry traffic, comprising multiple local ferry connections operating at regular intervals as well as international ferry routes linking Kiel with destinations such as Oslo and Göteborg. These routes are particularly relevant for modelling vessel interactions and traffic patterns in confined and highly trafficked waters.

3.2. Standardisation

A central objective of the preprocessing pipeline is the integration of multiple AIS data sources into a single, coherent dataset. To this end, all inputs are standardised to a unified schema, ensuring consistency across the two AIS data sources employed in this study. AIS transmissions comprise 27 distinct message types, with the primary distinction being between Class A and Class B messages (see

Table 1. Overview of AIS message classes and commonly used message types [51].

Message Class	Description	Message IDs
Class A	Position report	1, 2, 3
Class A	Static and voyage-related data	5
Class B	Position report	18, 19
Class B	Static data report	24

). Class A messages provide more detailed information and are mandatory for SOLAS-class vessels, including cargo ships, tankers, and commercial passenger vessels. In contrast, recreational craft and smaller commercial vessels are only required to transmit the more limited Class B messages.

Based on these message types, two relational tables are constructed. During this process, all navigational fields are standardised across data sources in accordance with the recommendations of the International Telecommunication Union [51].

The first, contains dynamic trajectory information that lies within the defined geographical area of interest (see

Table 2. Trajectory table containing dynamic AIS information.

Column	Description	Manually Entered
mmsi	MMSI	No
timestamp	UTC timestamp of the AIS message	No
lon	Longitude (EPSG:4326)	No
lat	Latitude (EPSG:4326)	No
status	Navigational status	Yes
cog	COG	No
heading	True heading	No
draught	Reported vessel draught	Yes

).

The second, serves as the vessel database and is constructed from static AIS reports. It stores vessel type and dimensional information required for geometric and interaction-aware modelling (see

Table 3. Static vessel information table.

Column	Description	Manually Entered
mmsi	MMSI	No
ship_type	AIS vessel type code	Yes
to_bow	Distance from GPS antenna to bow	Yes
to_stern	Distance from GPS antenna to stern	Yes
to_port	Distance from GPS antenna to port side	Yes
to_starboard	Distance from GPS antenna to starboard side	Yes

).

The static vessel metadata are further enriched using commercial web services (MyShipTracking) [52] for vessels with missing or incomplete entries. Invalid, inconsistent, or malformed AIS messages are discarded during this stage.

• Maps

To enrich AIS trajectories with additional environmental and navigational context, several geospatial data sources are incorporated. These include bathymetric information as well as polygon-based map layers extracted from the Overpass API (see Figure 1).

All positional data from these sources are transformed into a common geographic coordinate reference system (EPSG:4326) prior to further processing and feature extraction.

3.3. Trajectory Construction

Following standardisation, individual AIS messages are aggregated per MMSI and transformed into continuous vessel trajectories suitable for downstream analysis and prediction tasks. This stage focuses on organising temporally ordered position reports into coherent motion sequences while mitigating noise, irregular sampling, and artefacts inherent to AIS transmissions. The trajectory construction process consists of spatial and kinematic filtering, temporal segmentation into distinct movement episodes, smoothing and interpolation of vessel motion. Together, these steps yield structured trajectories that preserve navigational behaviour while remaining robust to measurement errors and reporting inconsistencies.

• Spatial and Kinematic Filtering

Trajectory construction begins with a naive aggregation of temporally ordered position reports for each unique MMSI. From these preliminary trajectories, physically implausible positions are identified and flagged. Such positions include reports located on land or exhibiting unrealistically high speeds.

While conventional AIS preprocessing pipelines typically employ a speed threshold of 30 kn for commercial vessels [53], this study adopts a threshold of 40 kn to accommodate high-speed patrol vessels operating in the Port of Kiel, which routinely exceed conventional merchant vessel speeds during security and surveillance operations.

For outlier detection, speed is not taken from the transmitted speed-over-ground field but is instead computed from consecutive spatial positions to ensure consistency across data sources.

Importantly, flagged outliers are not immediately removed but are retained as informative cues for subsequent trajectory segmentation. Removing isolated points prematurely can introduce additional artefacts when the underlying issue corresponds to a sustained positional jump rather than a single erroneous report.

• Trajectory Segmentation

AIS transmissions can be manually activated and deactivated, resulting in temporal gaps that lead to erroneous interpolations if not handled appropriately. In addition, AIS transmissions often remain active while vessels are moored, generating misleading motion artefacts during movement analysis.

To address these issues, a four-stage trajectory segmentation is applied to extract valid sub-trajectories for further preprocessing. The segmentation steps are applied iteratively and in the following order:

(i)

Outlier-based segmentation: Flagged outliers are used as potential split points. However, split trajectories are reconnected if the transition between neighbouring points (excluding the outlier) does not result in physically implausible speeds.

(ii)

Geospatial segmentation: Trajectories are split when they reach the boundary of the defined area of interest or enter a berthing area. This step separates local ferry routes and excludes stationary berthing manoeuvres.

(iii)

Observation gap segmentation: Trajectories are split when large temporal gaps between two reports occur. As straight trajectories can be interpolated more reliably than turning trajectories, the tolerated time gap varies between 2 and 5 min depending on the course of the trajectory.

(iv)

Motion-based segmentation: Trajectories are split when a vessel is assumed to be anchored. This condition is met if the vessel exhibits speeds below 0.3 kn for more than one hour or remains within a radius of 100 m for at least 5 min.

• Smoothing and Interpolation

AIS positions have been shown to deviate substantially from true vessel positions due to measurement noise and transmission errors [44]. To mitigate these effects, a Kalman filter with a constant-velocity motion model is applied to smooth vessel trajectories using position, speed, and course information [54]. Following smoothing, trajectories are interpolated using a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) [55]. Interpolation is performed on a fixed temporal grid with a step size of 5 s to align all trajectories in time, for consistent vessel interaction modelling. As interpolation can reintroduce invalid positions, such as points on land or unrealistically low-speed artefacts, the trajectory segmentation criteria for land proximity and stationary behaviour are re-applied as a final validation step.

All kinematic quantities derived from the trajectory—including speed, course, and Rate-of-Turn (ROT)—are computed from the interpolated position sequence rather than from the transmitted AIS fields. The broadcast ROT, SOG, and COG values are known to be unreliable in practice, as they depend on gyrocompass calibration, transmitter configuration, and update frequency. These frequently deviate substantially from the motion implied by consecutive positional fixes [44,56]. The position-derived kinematic features therefore constitute the sole reference representation used by all downstream components. Furthermore, the observation-gap segmentation step (see Section 3.3) applies a curvature-dependent gap tolerance—splitting trajectories at gaps exceeding 2 min during turning manoeuvres versus 5 min on straight segments—which prevents the constant-velocity Kalman model from being applied across extended high-ROT intervals.

Figure 2 provides a qualitative assessment of the pipeline’s behaviour under high-ROT conditions. Two representative 10 min trajectory segments from sailing vessels are shown; sailing vessels are selected because their frequent tacking manoeuvres—driven by wind conditions—produce multiple direction reversals within a single 10 min window, representing the most demanding case for the constant-velocity smoother. In each panel, blue dots indicate raw AIS position reports and the red line shows the fully preprocessed trajectory after Kalman smoothing and PCHIP interpolation. Across the two examples, the pipeline faithfully preserves the overall shape of the manoeuvres while suppressing positional noise, and the interpolated path connects observed positions without introducing spurious artefacts.

Figure 3 illustrates the cumulative effect of the complete preprocessing pipeline on a sample of 100 trajectories from the Port of Kiel area. The comparison clearly demonstrates the transformation from noisy, unstructured raw AIS position reports to clean, continuous vessel trajectories suitable for downstream machine learning tasks.

3.4. Train/Test Split Strategy

Prior to feature generation, the dataset is partitioned into training and test sets to prevent data leakage. Since vessel interactions are central for both the analysis and prediction tasks, splitting the data by MMSI is infeasible. Instead, the split is performed along the temporal dimension. This strategy introduces a trade-off between maintaining trajectory integrity and ensuring diversity across seasons, weekdays, and spatial regions in both subsets. To minimise trajectory fragmentation, data are split at midnight, a time period characterised by reduced maritime traffic. Individual dates are then randomly assigned to either the training or test set. For the Port of Kiel dataset, this approach results in fewer than 0.5% of trajectories being split.

Additionally, this temporal separation enables the combination of multiple AIS data sources without introducing duplicates or inconsistencies. In particular, high-resolution but temporally incomplete AIS data from Kiel University of Applied Science can be complemented with the lower-resolution but temporally continuous dataset provided by the DMA while maintaining a clean separation between training and test data, as illustrated in Figure 4.

3.5. Feature Generation

To obtain a feature-rich dataset, the processed vessel trajectories are enriched with contextual, kinematic, and interaction-based features.

• Geospatial Features

To provide additional environmental context, several geospatial features are computed for each trajectory point. These include the distance to the nearest shoreline, ferry route, and restricted navigation area, as well as the local water depth. In addition, historic vessel density maps are constructed from the trajectories in the training set. Separate density maps are generated for each vessel group as well as a global density map comprising all vessels. To improve generalisation, the density maps are smoothed using a Gaussian, as illustrated in Figure 5).

• Ship-level Features

From the interpolated trajectory positions, additional kinematic features are derived, including speed, acceleration, course, and rate of turn. On a per-sample basis, these derived features closely resemble the transmitted SOG and COG values and often exhibit smoother and more plausible behaviour. An exception occurs at very low speeds, where small positional fluctuations can lead to large variations in the derived course. In these cases, the transmitted course information is retained and used as a more reliable reference.

• Ship-to-Ship Interaction Features

Interactions between vessels are of particular interest for trajectory prediction and collision avoidance tasks. Therefore, additional interaction features are computed whenever two vessels are within a distance of 2 km of each other. These interaction features include relative motion characteristics such as relative speed, course, and bearing. Relative bearing is especially important for navigation, as it is a determining factor for right-of-way according to the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs).

Another key navigational metric is the Closest Point of Approach (CPA), which is defined as the point at which two vessels would reach their minimum separation distance if they were to maintain their current course and speed. Given the large variation in vessel dimensions within the confined waters of the Port of Kiel, vessel dimensions are incorporated into the computation of the Distance at Closest Point of Approach (DCPA) and the Time to Closest Point of Approach (TCPA) [57]. Since a small DCPA does not necessarily indicate a critical situation, for example, when vessels travel in parallel, a collision risk index based on [58] is employed. This provides a more reliable indication of which vessels are at risk of colliding and is defined as:

$$\mathrm{collision}\_\mathrm{risk}=\left(1-{\displaystyle \frac{\mathrm{TCPA}}{W_{\mathrm{tcpa}}}}\right)·\left(1-{\displaystyle \frac{\mathrm{DCPA}}{W_{\mathrm{dcpa}}}}\right).$$

(1)

TCPA and DCPA are normalised using weighting factors and clipped to the interval $[0,1]$. The weighting parameters $W_{\mathrm{tcpa}}$ and $W_{\mathrm{dcpa}}$ were selected based on interviews with navigation officers reported in the referenced study. The distance weighting factor is set to 500 m × 1.25, where 500 m is considered a safe passing distance in congested waters, with an additional 25% safety margin. The time weighting factor is set to 10 min and is further adjusted based on the relative angle of approach. Head-on encounters are considered less critical, as they are more easily detected by navigators and onboard systems [58], and therefore assigned a lower collision risk.

4. Representation Learning Models

To comprehensively evaluate the effectiveness of different representation learning paradigms in ship trajectory analysis, this paper presents a systematic comparison of seven deep learning models spanning three representative architectural categories:

• Convolution-based models, which capture local temporal dependencies through sliding receptive fields and are well suited for modelling short-term dynamic patterns;
• Transformer-based models, which employ attention mechanisms to model long-range temporal dependencies and global temporal relationships;
• Linear and lightweight sequence models, which enable efficient modelling of global temporal structures with reduced architectural complexity.

To ensure fairness and reproducibility, all models are implemented within a unified encoder–decoder representation learning framework and evaluated under consistent input/output definitions, training protocols, and experimental settings. Within this framework, Section 4.1 first formulates ship trajectory data in a mathematical manner and introduces the unified encoder–decoder architecture adopted in this work, including precise definitions of model inputs, latent feature representations, and reconstruction or prediction objectives. Subsequent subsections then describe the specific implementations and modelling characteristics of different representation learning methods within this unified framework.

4.1. Overall Architecture

• Ship Trajectory Definition

Ship trajectories are modelled as high-dimensional multivariate time series. Given a trajectory sample, it is represented as a matrix $\mathbf{X}\in {\mathbb{R}}^{L\times F}$, where L denotes the trajectory length and F denotes the feature dimension at each time step, including position, velocity, heading, and other navigation-related attributes. Let ${\mathbf{x}}_t\in {\mathbb{R}}^F$ denote the observation vector at time step t; then, the trajectory can be expressed as

$$\mathbf{X}=\left[\begin{array}{c}{\mathbf{x}}_1^{\top }\\ {\mathbf{x}}_2^{\top }\\ ⋮\\ {\mathbf{x}}_L^{\top }\end{array}\right]\in {\mathbb{R}}^{L\times F}.$$

(2)

During model training, trajectory data are provided in batches. Given a batch size B, a batch is denoted as $\mathcal{X}={\left\{{\mathbf{X}}_i\right\}}_{i=1}^B$, and the full dataset is represented as $\mathbb{D}={\left\{{\mathbf{X}}_i\right\}}_{i=1}^N$, where N denotes the total number of trajectory samples in the dataset. For trajectories with varying lengths, a fixed length L is adopted. Shorter sequences are zero-padded.

• Encoder and Latent Representation

Within the unified framework, all models share the same high-level structural definition. The encoder, denoted by $\mathcal{E}\left(·\right)$, maps an input trajectory $\mathbf{X}$ into a latent representation space:

$$\mathbf{Z}=\mathcal{E}\left(\mathbf{X}\right),$$

(3)

where $\mathbf{Z}$ represents a low-dimensional or high-level semantic representation of the trajectory, capturing ship motion patterns, temporal dependencies, and multivariate interactions. The primary differences among representation learning methods lie in the design of the encoder architecture, such as convolutional structures, attention mechanisms, or linear mappings.

• Decoder and Reconstruction Objective

The decoder $\mathcal{D}\left(·\right)$ takes the latent representation $\mathbf{Z}$ as input and produces a reconstructed trajectory $\widehat{\mathbf{X}}$:

$$\widehat{\mathbf{X}}=\mathcal{D}\left(\mathbf{Z}\right).$$

(4)

During the unsupervised representation learning stage, the model learns discriminative representations by minimising the reconstruction error between the input and reconstructed trajectories. The reconstruction objective is defined as

$$\underset{\theta }{min}{\mathcal{L}}_{\mathrm{ssl}}={∥\mathbf{X}-\widehat{\mathbf{X}}∥}_2^2,$$

(5)

where $\theta$ denotes all learnable parameters of the encoder and decoder. This reconstruction-based learning process does not rely on manual annotations and allows effective utilisation of large-scale unlabelled ship trajectory data.

• Classification Head and Representation Evaluation

To quantitatively assess the quality of the learnt trajectory representations, a lightweight classification head $\mathcal{C}\left(·\right)$ is introduced on top of the encoder output $\mathbf{Z}$, which predicts the behaviour category of each trajectory:

$$\widehat{\mathbf{y}}=\mathcal{C}\left(\mathbf{Z}\right).$$

(6)

In this setting, the classification task is used only during evaluation to examine the discriminative capability of the latent representations in downstream tasks, without altering the unsupervised training objective of the representation learning stage.

• Training Paradigm and Fine-tuning Strategies

A two-stage training paradigm of ”unsupervised pretraining + supervised fine-tuning” is adopted. First, the model is pretrained in an unsupervised manner using the trajectory reconstruction task to learn general-purpose trajectory representations. Subsequently, when a limited amount of labelled data is available, a classification head is added for fine-tuning. Two fine-tuning strategies are considered:

• Freeze Fine-tuning: the encoder parameters are kept fixed, and only the classification head is optimised;
• Joint Fine-tuning: the encoder and classification head are jointly optimised in an end-to-end manner.

This unified architecture provides a structurally aligned basis for comparing different representation learning methods, enabling a systematic analysis of their modelling capabilities and applicability in ship trajectory representation learning.

4.2. Temporal Convolutional Network

Temporal Convolutional Networks (TCNs) [59] extend one-dimensional CNNs to time-series modelling by capturing temporal dependencies through convolution operations along the time axis. Compared with recurrent models, convolution-based approaches enable efficient parallel computation and stable training, while shared kernels facilitate modelling recurring local temporal patterns.

Given an input sequence of length L, convolution kernel size $K_c$, stride S, and padding P, the output length after one-dimensional convolution is

$$L^{\prime }=⌊{\displaystyle \frac{L+2P-K_c}{S}}⌋+1.$$

(7)

At temporal position t, the convolution operation is defined as

$${\mathbf{z}}_t=\sum _{k=0}^{K_c-1}{\mathbf{W}}_k{\mathbf{x}}_{t·S+k-P},t=1,\dots ,L^{\prime },$$

(8)

where ${\mathbf{W}}_k$ denotes the convolution kernel parameters and ${\mathbf{z}}_t$ is the output representation at time step t. After linear projection or interpolation, the output sequence can be aligned to the original length L and used as the unified encoder output representation $\mathbf{Z}$.

While standard 1D-CNNs are effective at modelling local temporal patterns, their receptive field is limited by the kernel size, restricting the ability to capture long-range temporal dependencies. TCNs address this limitation by introducing dilated convolutions, which enlarge the receptive field without significantly increasing model complexity. For the lth TCN layer with dilation factor $d^{\left(l\right)}$ and kernel size $K_c$, the dilated convolution at time step t is computed as

$${\mathbf{Z}}_t^{\left(l\right)}=\sum _{k=0}^{K_c-1}{\mathbf{W}}_k^{\left(l\right)}{\mathbf{Z}}_{t-d^{\left(l\right)}k}^{(l-1)},$$

(9)

where ${\mathbf{Z}}^{(l-1)}$ denotes the feature representation from the previous layer. Causal padding is applied when indices fall outside the valid range to preserve temporal ordering. Under this formulation, the effective receptive field of a single TCN layer is given by

$$R^{\left(l\right)}=1+(K_c-1)d^{\left(l\right)}.$$

(10)

By stacking multiple dilated convolution layers with exponentially increasing dilation factors (e.g., $d^{\left(l\right)}=2^{l-1}$), the receptive field of a TCN grows exponentially with network depth, enabling modelling of long-range temporal dependencies.

In this work, a stride of $S=1$ together with appropriate padding is adopted, so that the output length of each layer matches the input length, allowing the TCN encoder to be seamlessly integrated into the unified time-series representation learning framework.

4.3. Linear Spatial–Temporal Feature Extractor

To enable efficient and practical representation learning for high-dimensional time-series data, this paper adopts Linear Spatial–Temporal Feature Extractor (LiST) [60] as a representative linear sequence modelling approach. LiST is designed to construct a lightweight encoder with spatio-temporal modelling capability while avoiding the high computational overhead of convolution and self-attention, making it well suited for large-scale, high-dimensional ship trajectory analysis.

In contrast to convolution-based or attention-based models, LiST is built entirely upon linear mappings, residual structures, and lightweight attention mechanisms. Its central idea is to apply linear feature transformations separately along the temporal and feature dimensions, thereby explicitly modelling temporal evolution patterns and multivariate interactions. This design substantially reduces model complexity while retaining the ability to capture discriminative spatio-temporal structural information.

Conceptually, LiST employs a dual-branch encoding scheme, corresponding to two different orders of spatio-temporal feature extraction: spatial → temporal and temporal → spatial. Given an input trajectory $\mathbf{X}$, the outputs of the two branches are formulated as

$${\mathbf{Z}}_{\mathrm{ref}}=\mathcal{T}\left(\mathcal{S}\left(\mathbf{X}\right)\right),{\mathbf{Z}}_{\mathrm{flip}}=\mathcal{S}\left(\mathcal{T}\left(\mathbf{X}\right)\right),$$

(11)

where $\mathcal{S}\left(·\right)$ and $\mathcal{T}\left(·\right)$ denote linear feature extraction modules along the feature and temporal dimensions, respectively. This dual-path design mitigates structural bias introduced by a single modelling order, leading to more robust spatio-temporal representations.

Finally, the outputs of the two branches are fused to produce a unified trajectory representation:

$${\mathbf{Z}}_{\mathrm{LiST}}={\mathbf{Z}}_{\mathrm{ref}}\oplus {\mathbf{Z}}_{\mathrm{flip}}\mathrm{or}{\mathbf{Z}}_{\mathrm{ref}}+{\mathbf{Z}}_{\mathrm{flip}},$$

(12)

where concatenation preserves richer structural information, while additive fusion offers higher computational efficiency in high-dimensional scenarios.

Overall, LiST does not aim to introduce complex nonlinear modelling, but instead achieves a balance between efficiency, stability, and representational capacity through an all-linear design. As a deployment-friendly spatio-temporal representation learning method, it provides effective latent representations for subsequent classification and analysis tasks.

4.4. Vanilla Transformer

Originally developed for natural language processing, the Transformer architecture is directly applied here to time-series data, where self-attention is performed across all time steps. The Vanilla Transformer [61] models dependencies among all temporal positions through self-attention, without relying on recurrent or convolutional structures. This design enables direct modelling of global temporal dependencies and supports fully parallel computation along the temporal dimension.

Given an input trajectory sequence $\mathbf{X}\in {\mathbb{R}}^{L\times F}$, the feature dimension is first projected to a model dimension D via a linear mapping, and positional embeddings are added to preserve temporal order information:

$${\mathbf{Z}}^{\left(0\right)}=\mathbf{X}{\mathbf{W}}^{\mathrm{in}}+\mathbf{E},{\mathbf{W}}^{\mathrm{in}}\in {\mathbb{R}}^{F\times D}.$$

(13)

In the lth Transformer encoder layer, the multi-head self-attention mechanism models interactions among time steps using queries (Query), keys (Key), and values (Value). For the hth attention head, the computation is given by

$${\mathbf{Q}}_h={\mathbf{Z}}^{(l-1)}{\mathbf{W}}_Q^{(l,h)},{\mathbf{K}}_h={\mathbf{Z}}^{(l-1)}{\mathbf{W}}_K^{(l,h)},{\mathbf{V}}_h={\mathbf{Z}}^{(l-1)}{\mathbf{W}}_V^{(l,h)},$$

(14)

and scaled dot-product attention is used to compute temporal correlation weights:

$${\mathbf{A}}_h=\mathrm{softmax}\left({\displaystyle \frac{{\mathbf{Q}}_h{\mathbf{K}}_h^{\top }}{\sqrt{D/H}}}\right),{\mathbf{O}}_h={\mathbf{A}}_h{\mathbf{V}}_h,$$

(15)

where H denotes the number of attention heads and $D/H$ is the dimension per head. The outputs of multiple attention heads are concatenated and linearly projected to form the output of the multi-head attention sublayer. Together with the Feed-Forward Network (FFN), residual connections, and layer normalisation, they constitute a Transformer encoder layer.

By stacking multiple encoder layers, a temporal latent representation $\mathbf{Z}\in {\mathbb{R}}^{L\times D}$ is obtained as the output of the unified encoder framework.

4.5. Denoising Autoencoder

Denoising Autoencoders (DAEs) [14] introduce noise perturbations at the input level and train an encoder–decoder model to reconstruct the clean sequence from the corrupted input, thereby promoting the learning of stable temporal semantics in the latent representation.

Given a trajectory sequence $\mathbf{X}\in {\mathbb{R}}^{L\times F}$, a noisy input is constructed as

$$\tilde{\mathbf{X}}=\mathbf{X}+ϵ,ϵ\sim \mathcal{N}(\mathbf{0},{\sigma }^2\mathbf{I}),$$

(16)

where $\sigma$ controls the noise magnitude (dae_noise). When a padding mask is present, noise is applied only to valid time steps.

DAE employs a Transformer Encoder–Decoder backbone. Through linear projection and positional encoding, $\tilde{\mathbf{X}}$ is mapped to a latent space and encoded into a representation $\mathbf{Z}\in {\mathbb{R}}^{L\times D}$, which is subsequently decoded to obtain the reconstructed sequence $\widehat{\mathbf{X}}\in {\mathbb{R}}^{L\times F}$.

The self-supervised objective minimises the denoising reconstruction error over valid time steps:

$${\mathcal{L}}_{\mathrm{ssl}}^{\mathrm{DAE}}={\lambda }_{\mathrm{rec}}{\displaystyle \frac{1}{{\sum }_{t=1}^L{m}_t}}\sum _{t=1}^L{m}_t{∥{\widehat{\mathbf{x}}}_t-{\mathbf{x}}_t∥}_2^2,$$

(17)

where $\mathbf{m}\in {\{0,1\}}^L$ denotes the valid time-step mask and ${\lambda }_{\mathrm{rec}}$ is the loss weight.

4.6. Evidential Autoencoder

Building upon the DAE, Evidential Autoencoders (EAEs) [13] further model the decoder outputs as parameters of an evidential distribution, thereby constraining not only the reconstruction mean but also the predicted uncertainty structure.

EAE adopts the same input perturbation scheme as DAE (Equation (16)) while producing Normal-Inverse-Gamma (NIG) parameters at the decoder. Given the latent representation $\mathbf{Z}\in {\mathbb{R}}^{L\times D}$ obtained from the Transformer encoder, the EAE decoder outputs four groups of NIG parameters:

$$(\mathit{\mu },\mathbf{v},\mathit{\alpha },\mathit{\beta })={\mathcal{D}}_{\mathrm{Trm}}\left(\mathbf{Z}\right),\mathit{\mu },\mathbf{v},\mathit{\alpha },\mathit{\beta }\in {\mathbb{R}}^{L\times F},$$

(18)

where $\mathit{\mu }$ represents the deterministic reconstruction mean and is directly used in downstream tasks while the remaining parameters characterise the evidence strength and distribution shape.

The self-supervised objective of EAE consists of an evidential negative log-likelihood and a regularisation term:

$${\mathcal{L}}_{\mathrm{ssl}}^{\mathrm{EAE}}={\lambda }_{\mathrm{nll}}{\mathcal{L}}_{\mathrm{nll}}+{\lambda }_{\mathrm{reg}}{\mathcal{L}}_{\mathrm{reg}},$$

(19)

where ${\mathcal{L}}_{\mathrm{nll}}$ denotes the average NIG negative log-likelihood over valid time steps, and ${\mathcal{L}}_{\mathrm{reg}}$ penalises excessive confidence. Specifically, the regularisation term is defined as

$${\mathcal{L}}_{\mathrm{reg}}=\mathbb{E}\left[{(\mathbf{X}-\mathit{\mu })}^2\odot (2\mathbf{v}+\mathit{\alpha })\right],$$

(20)

with the expectation computed only over valid time steps using the padding mask.

4.7. GroupMAE

GroupMAE is designed for high-dimensional ship trajectory sequences, where $\mathbf{X}\in {\mathbb{R}}^{L\times F}$ and F denotes the feature dimension. Its key characteristic is that masking is performed on feature groups, rather than individual feature dimensions, and the selected feature groups are masked consistently across all time steps.

Feature groups $\mathcal{G}=\{g_1,\dots ,g_G\}$ are constructed based on feature names, where each $g_j$ corresponds to a subset of feature indices. For each sample, $n_{\mathrm{mask}}$ groups are randomly selected for masking, as determined by the mask rate and the minimum number of masked groups. This results in a binary mask tensor $\mathbf{M}\in {\{0,1\}}^{L\times F}$, and the masked input is constructed as

$$\tilde{\mathbf{X}}=\mathbf{X}\odot (1-\mathbf{M}),$$

(21)

where ⊙ denotes element-wise multiplication. When a padding mask is present, masking is applied only to valid time steps, preventing padded positions from contributing to training.

GroupMAE adopts a Transformer Encoder–Decoder architecture to encode $\tilde{\mathbf{X}}$ into a latent representation $\mathbf{Z}\in {\mathbb{R}}^{L\times D}$ and decode it to obtain the reconstructed sequence $\widehat{\mathbf{X}}\in {\mathbb{R}}^{L\times F}$, as illustrated in Figure 6.

The reconstruction loss is computed only at masked positions:

$${\mathcal{L}}_{\mathrm{rec}}={\displaystyle \frac{1}{{\parallel \mathbf{M}\parallel }_1}}{∥(\widehat{\mathbf{X}}-\mathbf{X})\odot \mathbf{M}∥}_2^2,$$

(22)

where ${\parallel \mathbf{M}\parallel }_1$ denotes the number of masked elements over valid time steps.

To improve robustness under varying operating conditions, an additional Risk Extrapolation (REx) regularisation term is introduced. The core idea is to constrain the variance of reconstruction risk across different environments. Let the environment label of each sample be $e_i\in \{1,\dots ,E\}$, either provided by the data or constructed as pseudo-environments within a batch via quantile-based binning of input features.

The reconstruction risk for each environment e is computed as

$$r_e={\mathbb{E}}_{i:e_i=e}\left[{\mathcal{L}}_{\mathrm{rec}}\left({\mathbf{X}}_i\right)\right],$$

(23)

and a variance penalty is applied:

$${\mathcal{L}}_{\mathrm{rex}}=\mathrm{Var}\left({\left\{r_e\right\}}_{e=1}^E\right).$$

(24)

This regularisation encourages consistent reconstruction performance across environments, thereby discouraging reliance on environment-specific statistical cues.

The final Self-Supervised Learning (SSL) optimisation objective is

$${\mathcal{L}}_{\mathrm{ssl}}^{\mathrm{GroupMAE}}={\lambda }_{\mathrm{rec}}{\mathcal{L}}_{\mathrm{rec}}+{\lambda }_{\mathrm{rex}}{\mathcal{L}}_{\mathrm{rex}}.$$

(25)

5. Representation Learning Pipelines

Since different self-supervised encoders adopt heterogeneous learning objectives with distinct formulations and numerical scales, their self-supervised loss values are not directly comparable and thus cannot be used to quantitatively assess the quality of the learnt latent representations. To address this issue, this paper designs two interconnected yet purpose-specific representation learning pipelines, namely Pipeline 1 for fair encoder evaluation and optimal encoder selection and Pipeline 2 for high-quality representation extraction and structural analysis (see Figure 7).

In this section, the trajectory representation $\mathbf{X}\in {\mathbb{R}}^{L\times F}$ defined in Equation (2) is adopted by default, and the differences in data processing and training strategies across the two pipelines are clarified in detail.

5.1. Dataset Splitting Strategy

Given the complete ship trajectory dataset $\mathbb{D}={\left\{{\mathbf{X}}_i\right\}}_{i=1}^N$, the data are split into three mutually exclusive subsets following a $7:2:1$ ratio, namely the training set ${\mathbb{D}}_{\mathrm{tr}}$, the validation set ${\mathbb{D}}_{\mathrm{va}}$, and the test set ${\mathbb{D}}_{\mathrm{te}}$. The training set is used for parameter optimisation, the validation set for early stopping and hyperparameter selection, and the test set for final performance evaluation.

5.2. Pipeline 1: Encoder Evaluation and Optimal Hyperparameter Selection

The objective of Pipeline 1 is to compare the quality of latent representations learnt by different self-supervised encoders across a unified downstream task and to select the optimal encoder architecture and its corresponding hyperparameter configuration.

• Feature Debiasing

In the original feature space, a subset of features is directly or explicitly correlated with ship-type labels. Let the number of such features be denoted as M. In Pipeline 1, to prevent label information leakage and ensure a fair comparison among different encoders, a feature debiasing operation is applied to the input trajectories by removing these ship-type-related features, resulting in the debiased input

$${\mathbf{X}}^{\prime }\in {\mathbb{R}}^{L\times (F-M)}.$$

(26)

The specific features removed ($M=6$) and the full input feature inventory ($F=35$) are listed in

Table A4. Complete model input feature set and debiasing for Pipeline 1. All features are present at every observation timestamp. Cyclic features use sin/cos encoding; categorical features use one-hot encoding. Features marked “Excluded“ are removed under the debiasing procedure (Section 5.2, Equation (26)) to prevent ship-group label leakage in Pipeline 1. The Ship DB dimension columns to_bow, to_stern, to_port, and to_starboard are collapsed into length and width during feature engineeringreferences and are therefore covered by their exclusion.

Feature	Group	Encoding	Pipeline 1 Status
Trajectory features
lon	Trajectory	–	Retained
lat	Trajectory	–	Retained
x	Trajectory	–	Retained (projected)
y	Trajectory	–	Retained (projected)
rel_x	Trajectory	–	Retained (segment-relative)
rel_y	Trajectory	–	Retained (segment-relative)
status	Trajectory	one-hot	Retained
speed	Trajectory	–	Retained
acc	Trajectory	–	Retained
course	Trajectory	sin/cos	Retained
angular_difference	Trajectory	sin/cos	Retained
Static vessel features
ship_type	Static	one-hot	Excluded—direct class label
ship_group	Static	one-hot	Excluded—direct class label
length	Static	–	Excluded—class-discriminative dimension
width	Static	–	Excluded—class-discriminative dimension
Map/environment features
water_depth	Map	–	Retained
dist_to_land	Map	–	Retained
dist_to_ferry_route	Map	–	Retained
dist_to_restricted_area	Map	–	Retained
density_all	Map	–	Retained
density_own_group	Map	–	Excluded—label-derived proxy
Ship-to-ship interaction features
dist	Ship2ship	–	Retained
rel_speed	Ship2ship	–	Retained
course_diff	Ship2ship	sin/cos	Retained
rel_bearing	Ship2ship	sin/cos	Retained
rel_bearing_cat	Ship2ship	one-hot	Retained
tcpa	Ship2ship	–	Retained
dcpa	Ship2ship	–	Retained
collision_risk	Ship2ship	–	Retained
ship_type_other	Ship2ship	one-hot	Excluded—encodes class of interaction partner
ship_group_other	Ship2ship	one-hot	Retained
Datetime features
day_of_year	Datetime	sin/cos	Retained
day_of_week	Datetime	sin/cos	Retained
hour_of_day	Datetime	sin/cos	Retained
month_of_year	Datetime	sin/cos	Retained
Total features		35 full set; 29 retained in Pipeline 1 ($M=6$ excluded)

in Appendix A.

This operation ensures that the encoders learn representations purely from kinematic and dynamic motion patterns, such that the resulting latent representation $\mathbf{Z}=\mathcal{E}\left({\mathbf{X}}^{\prime }\right)$, which is defined in Equation (3), faithfully reflects the temporal modelling capability of the encoder.

• Stage 0: Self-Supervised Learning Pretraining

In Stage 0, the unified encoder–decoder framework introduced in the previous sections is adopted. Given an input trajectory ${\mathbf{X}}^{\prime }$, the encoder maps the input to a latent representation,

$$\mathbf{Z}=\mathcal{E}\left({\mathbf{X}}^{\prime }\right),$$

(27)

which is subsequently processed by the corresponding decoder $\mathcal{D}\left(·\right)$ or prediction head, depending on the specific SSL paradigm. Each encoder is trained by minimising its own SSL objective,

$$\underset{{\theta }_{\mathcal{E}}^{\left(m\right)},{\theta }_{\mathcal{D}}^{\left(m\right)}}{min}{\mathcal{L}}_{\mathrm{ssl}}^{\left(m\right)},$$

(28)

where ${\mathcal{L}}_{\mathrm{ssl}}^{\left(m\right)}$ denotes the self-supervised loss of the mth encoder (e.g., reconstruction loss, denoising loss, masked modelling loss, or evidential loss). This stage is performed without using any ship-type labels. Different encoders (TCN, LiST, Transformer, DAE, EAE, GroupMAE, etc.) are trained independently, resulting in pretrained encoder parameters ${\theta }_{\mathcal{E}}^{\left(m\right)}$.

• Stage 1: Frozen Encoder Supervised Evaluation

In Stage 1, the encoder parameters are frozen,

$$\mathcal{E}(·;{\theta }_{\mathcal{E}}^{\left(m\right)})\mathrm{fixed},$$

(29)

and a lightweight classification head is introduced on top of the latent representation $\mathbf{Z}$. The supervised mapping defined in Equation (6) is adopted for ship-type prediction. The classification head is trained by minimising the supervised classification loss,

$$\underset{{\theta }_{\mathcal{C}}}{min}{\mathcal{L}}_{\mathrm{cls}},$$

(30)

while keeping the encoder unchanged. Model optimisation is performed on the training set ${\mathbb{D}}_{\mathrm{tr}}$, and the validation set ${\mathbb{D}}_{\mathrm{va}}$ is used for early stopping and hyperparameter selection. This stage evaluates the discriminative power of the learnt representation $\mathbf{Z}$ without altering the encoder, ensuring that performance differences primarily reflect the quality of the encoder itself rather than the capacity of the classifier.

• Stage 2: Joint Fine-tuning

In Stage 2, both the encoder and the classification head are jointly optimised in an end-to-end supervised manner. Specifically, the following objective is minimised:

$$\underset{{\theta }_{\mathcal{E}}^{\left(m\right)},{\theta }_{\mathcal{C}}}{min}{\mathcal{L}}_{\mathrm{cls}}.$$

(31)

Training is conducted on the training set ${\mathbb{D}}_{\mathrm{tr}}$, while the validation set remains responsible for early stopping and model selection. Final performance is reported exclusively on the test set ${\mathbb{D}}_{\mathrm{te}}$. This stage assesses the adaptability of each encoder under supervised fine-tuning and provides an upper bound on downstream performance.

• Hyperparameter Optimisation and Encoder Selection

For each encoder architecture, hyperparameter optimisation is performed using the Tree-structured Parzen Estimator (TPE) implemented in the Optuna framework [62]. The optimisation objective is the validation classification accuracy obtained in Stage 1. By performing hyperparameter grid search (e.g., latent dimension, network depth, mask ratio, noise level) and comparing supervised performance across Stage 1 and Stage 2, Pipeline 1 selects the optimal encoder and its corresponding hyperparameter configuration, denoted as

$$({\mathcal{E}}^{\star },{\theta }^{\star }),$$

(32)

where ${\mathcal{E}}^{\star }$ represents the selected encoder architecture and ${\theta }^{\star }$ denotes its optimal hyperparameter set.

5.3. Pipeline 2: Representation Extraction and Structural Analysis

Pipeline 2 builds upon the optimal encoder ${\mathcal{E}}^{\star }$ selected by Pipeline 1 and shifts the focus from encoder comparison to representation analysis. Its objective is to extract high-quality latent representations and investigate their intrinsic structural and interpretable properties.

• Full Feature Space

Unlike Pipeline 1, Pipeline 2 operates on the complete trajectory representation $\mathbf{X}\in {\mathbb{R}}^{L\times F}$, including all kinematic, contextual, and ship-type-related features. This enables the encoder to leverage the full richness of the input data and produce representations that are optimally suited for downstream behavioural analysis and clustering tasks.

• Stage 0: Self-Supervised Learning Pretraining

Using the optimal hyperparameters identified in Pipeline 1, SSL training is performed using the original trajectory representation $\mathbf{X}$ with the complete feature space, and only the training set ${\mathbb{D}}_{\mathrm{tr}}$ is employed. The encoder is trained by minimising its corresponding self-supervised objective,

$$\mathbf{Z}={\mathcal{E}}^{\star }\left(\mathbf{X}\right),\underset{{\theta }_{\mathcal{E}}^{\star }}{min}{\mathcal{L}}_{\mathrm{ssl}}^{\star },$$

(33)

without involving ship-type labels in any part of the training process. Early stopping is applied based on the validation reconstruction loss. Upon convergence, the encoder is used to extract latent representations for all trajectories in the dataset:

$${\mathbf{Z}}_i={\mathcal{E}}^{\star }\left({\mathbf{X}}_i\right),i=1,\dots ,N.$$

(34)

After training, the resulting latent representation $\mathbf{Z}$ is used for subsequent unsupervised analyses, including clustering, embedding-space visualisation, and post hoc comparison with ship-type labels, in order to reveal intrinsic ship-type structures and other interpretable motion patterns captured by the learnt representations.

• Embedding Clustering as a Behavioural Structure Probe

Clustering serves as an operational probe to assess how well different feature spaces capture interpretable behavioural organisation in AIS data. We consider two complementary feature spaces: (i) the learnt embedding space $\mathbf{z}\in {\mathbb{R}}^D$ produced by ${\mathcal{E}}^{\star }$ (e.g., $D=128$) and (ii) an expert-designed feature space derived from commonly used nautical descriptors, including SOG, COG, turn rate, and proximity to ports or fairways. This dual-view design enables direct comparison between the behavioural structures induced by representation learning and those encoded by domain-driven features.

• Stage 1: Unsupervised Clustering Analysis

To investigate the behavioural structure encoded in the latent space, unsupervised clustering is performed on the extracted representations ${\left\{{\mathbf{Z}}_i\right\}}_{i=1}^N$. AIS trajectories exhibit non-linear, multi-modal structure, elongated corridors, branching patterns, heterogeneous density, and substantial noise. To accommodate these properties, Pipeline 2 focuses on density-based and graph-based clustering models capable of recovering arbitrarily shaped clusters, robustly handling heterogeneous density, and naturally supporting noise/outlier treatment.

Multiple clustering algorithms are evaluated, including Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) [63], Variational Bayesian Gaussian Mixture Model (VBGMM) [64], k-nearest neighbour graph with Leiden community detection [65], and First Integer Neighbour Clustering Hierarchy (FINCH) [66]. The specific models considered are summarised in

Table 4. Clustering models considered in Pipeline 2 for behavioural analysis.

Model	Core Assumptions	Fitness for Maritime Behaviour
HDBSCAN [63]	Clusters are high-density regions separated by low density. No assumptions about cluster number or shape.	Excellent for arbitrary-shape behaviour modes and noise handling. Hierarchical structure enables multi-scale analysis of local manoeuvres and global routes.
VBGMM [64]	Gaussian mixture components with VB inference automatically determining effective number of clusters.	High. Mixture components approximate complex distributions. Probabilistic nature valuable for anomaly detection and modelling speed/heading variability.
k-NN + Leiden [65]	Dense feature-space regions correspond to densely connected graph communities.	Excellent for interconnected route networks. Connectivity guarantee prevents fragmented clusters and improves stability.
FINCH [66]	Shared nearest neighbour relationships form hierarchical multi-scale patterns.	High. Hierarchical approach suits multi-scale behaviours. Parameter-free (except k) and robust for exploratory clustering.

.

For each clustering method, hyperparameter tuning is conducted to optimise the Density-Based Clustering Validation (DBCV) score [67], which measures the quality of density-based cluster separation. The resulting cluster assignments are analysed to assess:

• The semantic interpretability of discovered behaviour modes;
• The alignment between learnt clusters and expert-defined vessel categories;
• The robustness of cluster structure across different clustering algorithms.

• Clustering Validation Metrics

To compare clusterings across feature spaces and models, we employ two complementary categories of metrics: (i) intrinsic density/graph-based metrics suited to non-spherical clusters (DBCV, Conductance, Modularity), which measure cluster quality without requiring ground-truth labels, and (ii) traditional centroid-based metrics (Silhouette, Calinski–Harabasz, Davies–Bouldin) provided as baseline references, though these assume convex cluster geometry less appropriate for maritime trajectories. The intrinsic metrics are prioritised because clustering serves as an operational probe of representation quality rather than a classification task, focusing on discovering latent behavioural structure naturally encoded in the representation space. Key intrinsic metrics and their interpretations are summarised in Table 5.

• Dimensionality Reduction for Visualisation

To facilitate visual inspection of the learnt representations, the high-dimensional latent embeddings $\mathbf{Z}\in {\mathbb{R}}^D$ are projected into a two-dimensional space using Uniform Manifold Approximation and Projection (UMAP) [68]. UMAP is a manifold learning technique that preserves both local and global structure, making it well suited for visualising cluster separation and topological relationships in the embedding space.

The two-dimensional projections are colour-coded by cluster assignment and vessel type, enabling qualitative assessment of representation quality and behavioural coherence.

Table 5. Key clustering metrics used in Pipeline 2, with emphasis on intrinsic density/graph-based metrics.

Metric	Type	What It Measures	Preferred Direction
DBCV [67]	Density-intrinsic	Density connectivity within clusters versus density separation between clusters using a density-based distance.	Higher is better.
Conductance [69]	Graph-intrinsic	Edge-cut quality: internal connectivity of a cluster relative to its boundary with the rest of the graph.	Lower is better.
Modularity [65,69]	Graph-intrinsic	Strength of community division relative to a random-graph expectation; primary optimisation objective in Leiden community detection.	Higher is better.

Table 5. Key clustering metrics used in Pipeline 2, with emphasis on intrinsic density/graph-based metrics.

Metric	Type	What It Measures	Preferred Direction
DBCV [67]	Density-intrinsic	Density connectivity within clusters versus density separation between clusters using a density-based distance.	Higher is better.
Conductance [69]	Graph-intrinsic	Edge-cut quality: internal connectivity of a cluster relative to its boundary with the rest of the graph.	Lower is better.
Modularity [65,69]	Graph-intrinsic	Strength of community division relative to a random-graph expectation; primary optimisation objective in Leiden community detection.	Higher is better.

6. Experiments

This section evaluates self-supervised representation learning methods adopted for AIS-based trajectory data under a unified experimental protocol and analyses the intrinsic structure of the learnt representation space. Because the considered self-supervised objectives are heterogeneous and their loss values are not directly comparable, model selection is performed using common downstream task (Pipeline 1), followed by an unsupervised structural analysis of the learnt representation (Pipeline 2).

6.1. Experimental Setup

• Post-processing Experimental Dataset and Unified Data Load

We conduct all experiments on a processed AIS trajectory dataset covering the port of Kiel and surrounding waters, extracted from the year 2022–2023 AIS streams.

The processes trajectories are presented on a fixed temporal grid with sampling interval of 5 s, and interactions are computed when vessels are within 2 km, to keep the interaction input size fixed; only the two neighbours with the highest collision-risk score are retained per time step. After applying the comprehensive processing pipeline described in Section 3 (Contribution 1), the dataset comprises 176,787 cleaned trajectories from 9948 unique vessels. The complete post-processed feature set used in the experiments—including static ship-, dynamic ship-, and pairwise ship-to-ship— is listed in Appendix A.

Table 6. Post-processed dataset summary used for experiments.

Item	Value
Region of interest	Port of Kiel and surrounding waters (($10.12°$ E, $54.31°$ N), ($10.33°$ E, $54.46°$ N))
Time span	730 days, 2022–2023
Temporal resolution (post-processing)	5 s (fixed temporal grid)
Segment length for learning	$L=120$ time steps (10 min)
Trajectories (after processing)	176,787
Unique vessels (MMSI)	9948
Total interpolated points	63,448,367
Total segments	527,225
Interaction range	2 km
Neighbour retention	Top 2 neighbours by collision-risk score
Feature definitions	See Appendix A

summarises the key characteristics of the post-processed dataset and the sampling strategy employed in both experiments.

The unified data loader constructs learning samples by segmenting the post-processed 176,787 trajectories (already on a 5 s temporal grid) into fixed-length sequences of $L=120$ time steps, equivalent to 10 min of vessel movement without overlap. This segmentation procedure yields 527,225 trajectory segments that serve as the fundamental unit of analysis in both experiments.

At each time step, ship-to-ship interaction features are available for vessels within 2 km, with only the two neighbours exhibiting the highest collision-risk score retained to maintain fixed input dimensionality.

Shorter segments are zero-padded and accompanied by a binary mask to ensure that padded values do not contribute to training objectives or evaluation metrics.

All continuous features are subjected to Z-score standardisation. The mean and standard deviation were computed exclusively from the training set to prevent information leakage, and subsequently applied to the training, validation, and test sets.

Periodic angular features, such as course, heading, relative bearing are encoded using sine and cosine transforms to avoid discontinuities at wrap-around points (e.g., $0^{\circ }\equiv {360}^{\circ }$).

• Dataset splitting and leakage contro

We split the 527,225 segments into training (${\mathcal{D}}_{tr}$), validation (${\mathcal{D}}_{va}$), and test (${\mathcal{D}}_{te}$) sets with a [7:2:1] ratio. To prevent information leakage in the segment-based split or shared interaction features, all segments sharing the same trajectory identifier (traj_id) or overlapping temporal windows are assigned to the same subset. This ensures that no interaction scene is fragmented across training and evaluation splits, maintaining the integrity of temporal dependencies and vessel-specific behaviour patterns. The validation set ${\mathcal{D}}_{va}$ is used exclusively for hyperparameter selection and early stopping in Experiment I (Section 6.2), while the test set ${\mathcal{D}}_{te}$ is held out for final performance reporting. For Experiment II (Section 6.3), clustering is performed on a fixed random sample of 50,000 segments drawn from the combined dataset to ensure computational reproducibility across representations and methods.

• Experimental scope and evaluation strategy

The remainder of this section presents two complementary experiments aligned with the dual-pipeline evaluation methodology (Contribution 6).

Experiment I (Section 6.2) implements the three-stage representation learning framework (Contribution 2):

• Stage 0: self-supervised pretraining with hyperparameter optimisation conducted exclusively on self-supervised validation loss.
• Stage 1: linear probe evaluation to isolate representation quality from classifier capacity.
• Stage 2: full fine-tuning as an upper-bound reference.

This workflow benchmarks three encoder architectures under the ship-type classification probing task. The three proposed methods, GMAE with environment-aware learning via REx (Contribution 3) and semantic feature grouping through group-wise masking (Contribution 4), EAE with uncertainty-aware representations via evidential regression, and DAE as a denoising baseline, and three established baselines, Transformer, TCN, and LiST, are used to establish comparative performance across architectural paradigms.

Experiment II (Section 6.3) employs unsupervised clustering with explicit assessment of intrinsic structure quality (Contribution 6) to validate whether learnt representations naturally organise trajectory segments into coherent behavioural groups aligned with operational context.

Together, these experiments establish representation quality through both discriminative power (supervised probing) and interpretable structure (unsupervised discovery), providing comprehensive validation of the proposed framework’s ability to learn robust representations that generalise across diverse environmental conditions.

6.2. Experiment I: Supervised Probing for Encoder Selection

• Scope and evaluation protocol

This experiment evaluates the three-stage representation learning framework (Contribution 2) by benchmarking six self-supervised encoder architectures under a unified downstream task: ship-type prediction.

We compare three proposed methods (GMAE-REx, EAE, DAE) against three established baselines (Transformer, TCN, LiST) to establish which architectural approach yields the most discriminative trajectory representations when only limited supervision is available.

• Feature debiasing for fair encoder comparison

To ensure a fair comparison on the ship-type probing task and avoid trivial shortcuts, ship-type indicative static attributes are removed or neutralised following the debiasing procedure in Section 5.2. The complete list of all 35 input features and the six features excluded under this procedure are detailed in Table A4 (Appendix A). This debiased input is used consistently across all encoders in Pipeline 1. For consistency across pipelines, the same debiasing is also applied when constructing the expert-selected feature representation in Pipeline 2. As a result, performance differences primarily reflect how representations capture motion and interaction patterns, rather than memorising vessel metadata that directly encodes ship type.

• Environment-aware learning

The benchmarked encoders include GMAE-REx, which combines semantic feature grouping with REx regularisation (Contribution 3) to penalise reconstruction strategies favouring particular environmental conditions, and EAE, which provides uncertainty-aware representations through evidential regression that distinguishes epistemic from aleatoric uncertainty. DAE serves as a denoising reconstruction baseline, providing a strong reference point for evaluating the additional benefits of environment-aware learning (GMAE-REx) and uncertainty quantification (EAE).

Three established baseline encoders—Transformer (attention-based), TCN (convolution-based), and LiST (linear projection)—provide comparative reference points across different architectural paradigms.

These design choices directly address the environmental heterogeneity and domain shift challenges outlined in the introduction, enabling learning of representations that remain valid across distributional shifts between training and deployment scenarios.

• Hyperparameter optimisation

Following Contribution 2, hyperparameters are optimised using Optuna [62] with TPE sampling over the search space defined in

Table 7. Hyper-parameter search space for encoder selection (Experiment I). Following Contribution 2, optimisation is conducted exclusively on self-supervised validation loss.

Hyper-Parameter		Optuna Search Space
Batch size	$batch\_size$	$[32,64,128]$
Learning rate	$lr$	$0.001$ (fixed)
Encoder layers	$e_{layers}$	$[1,2,3,4,5]$
Decoder layers	$d_{layers}$	$[1,2,3,4,5]$
Model dimension	$d_{model}$	$[32,64,128]$
FFN dimension	$f_{dim}$	$[64,128,256,512,1024]$
Attention heads	$n_{heads}$	$[2,4,8]$
Dropout	$dropout$	$[0.0,0.1,0.3]$
Noise (DAE/EAE only)	$noise$	$[0.01,0.02,0.05,0.1]$

, with selection based exclusively on validation accuracy. For each encoder, we run 30 Optuna trials and select the configuration with the highest Stage 2 validation accuracy on ${\mathcal{D}}_{va}$ with early stopping.

Across all runs, we optimise with Rectified Adam (RAdam) [70] (learning rate $1\times {10}^{-3}$), train for up to 50 epochs, and apply early stopping with patience of 5 epochs.

• Ablation and sensitivity analysis for GMAE-REx

To understand the contribution of the main design choices in GMAE-REx, we conduct a one-factor-at-a-time ablation under the same three-stage protocol (SSL pretraining → linear probe → fine-tune) and report both linear-probe accuracy (representation quality) and fine-tune accuracy (downstream-task performance).

• Sensitivity to group mask ratio

Table 8. Sensitivity to group mask ratio (levelA, density4), ${\lambda }_{\mathrm{rex}}=0.1$.

Mask Ratio (Group Mask)	0.25	0.35	0.50	0.75
Linear Probe (Acc.)	0.7447	0.7447	0.7535	0.7479
Fine-tune (Acc.)	0.8514	0.8514	0.8548	0.8524

sweeps the group mask ratio under the coarse grouping scheme with env scheme = density4 and ${\lambda }_{\mathrm{rex}}=0.1$. Overall, moderate masking yields competitive probe accuracy, while downstream fine-tuning remains stable across a wide range of mask ratios.

• Grouping granularity (levelA vs. levelB)

We define two semantic grouping granularities for group-wise masking. levelA is a coarse partition that aggregates features into a small number of robust blocks (e.g., time, kinematics, geo/map, density, interaction/risk, shape, and categorical/meta), while levelB further refines these blocks into sub-groups (e.g., hour/day/month time cycles, heading/ course vs. speed/acc motion, absolute vs. relative coordinates, global vs. group-specific density, and risk vs. bearing vs. relative-motion interaction features). This design allows us to control the strength and structure of the masked reconstruction task: levelA emphasizes broad cross-group dependencies, whereas levelB provides a more structured masking target and typically yields a richer reconstruction signal for invariance regularisation. We next compare the coarse semantic grouping (levelA) to a finer-grained grouping (levelB) while fixing group mask rate = 0.5, env scheme = density4, and ${\lambda }_{\mathrm{rex}}=0.1$. As shown in

Table 9. Grouping scheme ablation (group mask rate = 0.5, env scheme = density4, ${\lambda }_{\mathrm{rex}}=0.1$).

Group Scheme	levelA	levelB
Linear Probe (Acc.)	0.7447	0.7474
Fine-tune (Acc.)	0.8517	0.8556

, levelB consistently improves downstream fine-tuning, suggesting that more structured feature partitions provide a stronger reconstruction signal and a more informative invariance regularisation target.

• Environment scheme

Table 10. Environment scheme ablation (group scheme = levelB, group mask rate = 0.5, ${\lambda }_{\mathrm{rex}}=0.1$).

Env Scheme	density4	geo4	densitygeo16	densityhour16
Linear Probe (Acc.)	0.7447	0.7495	0.7444	0.7484
Fine-tune (Acc.)	0.8517	0.8508	0.8513	0.8526

evaluates different pseudo-environment definitions for REx under group scheme = levelB, group mask rate = 0.5, and ${\lambda }_{\mathrm{rex}}=0.1$. We observe small but consistent differences: incorporating temporal proxies (e.g., densityhour16) slightly improves fine-tune accuracy, while the simpler density4 remains a strong default with minimal partitioning complexity.

• Strength of REx regularisation

Finally, we ablate ${\lambda }_{\mathrm{rex}}$ under group scheme = levelB, group mask rate = 0.5, and env scheme = densityhour16.

Table 11. REx weight ablation (group scheme = levelB, group mask rate = 0.5, env scheme = densityhour16).

${\mathit{\lambda }}_{\mathbf{rex}}$	0.0	0.05	0.1	0.2
Linear Probe (Acc.)	0.7454	0.7510	0.7447	0.7437
Fine-tune (Acc.)	0.8515	0.8547	0.8517	0.8513

suggests that a mild invariance penalty is beneficial (${\lambda }_{\mathrm{rex}}=0.05$), while stronger regularisation may slightly degrade both probe and fine-tune performance.

• Selected configuration

Based on the above ablations, we choose group scheme = levelB with a strong group masking (group mask rate = 0.5) and the environment partition from the combination of density and hours (densityhour16) with ${\lambda }_{\mathrm{rex}}=0.05$ as the default setting. This configuration achieves the best fine-tune accuracy in our sweep and is used as the reference GMAE-REx setup in subsequent experiments.

• Results and selected encoder

Table 12. Best hyperparameter configurations and validation accuracy for each encoder (Experiment I). GMAE-REx (Contributions 3–4) achieves the best performance, outperforming all baseline architectures. Trainable parameter counts (Params) are reported for the best-found configuration of the hyperparameters found in Table 7.

HParam	GMAE-REx	DAE	EAE	TCN	Transformer	LiST
$batch\_size$	32	64	128	32	32	32
$lr$	$0.001$	$0.001$	$0.001$	$0.001$	$0.001$	$0.001$
$e_{layers}$	3	4	5	3	3	3
$d_{layers}$	3	4	3	1	1	1
$d_{model}$	128	64	64	128	128	128
$f_{dim}$	256	512	512	–	–	–
$n_{heads}$	4	8	4	–	4	–
$dropout$	$0.1$	$0.1$	$0.1$	$0.1$	$0.1$	$0.1$
$noise$	–	$0.01$	$0.05$	–	–	–
Params	≈1.01 M	≈0.74 M	≈0.74 M	≈25 K	≈0.58 M	≈0.60 M
Validation Accuracy	$\mathbf{86.03}$%	$85.63\%$	$85.56\%$	$76.27\%$	$84.93\%$	$85.12\%$

reports the best hyperparameters and corresponding validation accuracy for each encoder. GMAE-REx achieves the highest validation accuracy ($86.03\%$), outperforming all baselines: transformer-based (DAE: $85.63\%$, EAE: $85.56\%$, Transformer: $84.93\%$), linear (LiST: $85.12\%$), and convolution-based (TCN: $76.27\%$). The superior performance of GMAE-REx validates the effectiveness of combining semantic feature grouping (Contribution 4) with environment-aware learning via REx regularisation (Contribution 3), which encourages representations that generalise across varying traffic densities, geographical contexts, and temporal conditions rather than memorising environment-specific statistical cues. GMAE-REx is therefore selected as the final encoder, denoted by $(E^{\star },{\theta }^{\star })$, and used in Experiment II for unsupervised structural analysis.

6.3. Experiment II: Unsupervised Clustering for Structural Discovery

• Scope and evaluation objective

This experiment implements the unsupervised component of the dual-pipeline evaluation methodology (Contribution 6), employing clustering to validate whether learnt representations naturally organise trajectories into interpretable behavioural groups aligned with operational context—without relying on manual annotations. Clustering serves as an operational probe of representation quality because maritime navigation exhibits multi-modal behaviour arising from heterogeneous factors (traffic regulations, bathymetry, vessel intent), and regions of high trajectory density often correspond to semantically recognisable structures such as traffic lanes, anchorage zones, and manoeuvring areas. We compare learnt embeddings extracted from the encoder selected in Experiment I (GMAE-REx) against expert-selected nautical features (Contribution 7) to assess whether representations learnt via the proposed framework (Contributions 2–5) capture behavioural structure that extends beyond domain-engineered features.

• Clustering backends and design rationale

We evaluate four clustering methods selected for their complementary strengths in capturing complex, non-linear structures characteristic of maritime navigation, as summarised in

Table 13. Clustering methods used for Experiment II and their fitness for maritime trajectory analysis. Detailed descriptions and mathematical formulations are provided in Appendix B.

Method	Key Characteristics	Fitness for AIS Behaviour
kNN-Leiden	Graph-based community detection via modularity optimisation with guaranteed connectivity [65].	Excellent for route-network structures and heterogeneous density; connectivity guarantee reduces fragmentation.
HDBSCAN	Hierarchical density-based clustering with explicit noise handling via mutual reachability [63].	Excellent for arbitrary-shape clusters and anomaly detection; multi-scale structure captures local maneuvers and global patterns.
VBGMM	Variational Bayesian Gaussian Mixture with automatic component selection [71].	High fitness for overlapping behaviours and uncertainty quantification; aligns with Contribution 5.
FINCH	Parameter-free hierarchical clustering via first-neighbour relations [66].	High fitness for exploratory multi-scale analysis; minimal tuning required.

.

kNN-Leiden constructs a k-nearest neighbour graph and applies modularity-based community detection with guaranteed connectivity, suitable for route-network structures with heterogeneous density. HDBSCAN builds a hierarchical density model and selects stable clusters while explicitly identifying noise (anomalous trajectories), enabling multi-scale analysis of local manoeuvres and global patterns. VBGMM employs variational Bayesian inference with automatic component selection, providing probabilistic assignments and uncertainty quantification that align with the framework’s emphasis on uncertainty-aware representations (Contribution 5). FINCH offers parameter-free hierarchical clustering, enabling exploratory multi-scale analysis with minimal tuning.

Table 14. Distance metrics and optimisation objectives for each clustering method and representation (Experiment II).

Method	Distance Metric	Optimisation Objective
kNN-Leiden	Cosine	Modularity
HDBSCAN	Euclidean	DBCV
VBGMM	Probabilistic	ELBO
FINCH	Cosine	Silhouette

lists the distance metrics and optimisation objectives for each method–representation pair.

• Two-stage hyperparameter optimisation

For each clustering method and representation, we follow a two-stage optimisation procedure, with random seeds fixed for reproducibility, to balance exploration and computational efficiency. Stage 1 (Rough optimisation): Optuna with TPE sampling explores the search space defined in

Table 15. Optuna search space for Stage 1 rough hyperparameter optimisation (Experiment II).

Method	Hyperparameter	Optuna Search Space
kNN-Leiden	n_neighbors	[10, 50]
	resolution	[0.5, 2.0], step 0.1
HDBSCAN	min_cluster_size	[20, 200], step 5
	min_samples	[5, 50]
	cluster_selection_epsilon	[0.0, 1.0], step 0.05
VBGMM	n_components	[5, 25]
	weight_concentration_prior	[0.001, 1.0]
	mean_precision_prior	[0.0001, 0.1]
FINCH	n_neighbors	[10, 50]

on a subset of 500 samples.

Stage 2 (Fine optimisation): A focused grid search refines the Optuna solution on the same 500-sample subset using the centred grid defined in

Table 16. Grid search space for Stage 2 fine hyperparameter optimisation (Experiment II). Each range is centred around the Optuna optimum.

Method	Hyperparameter	Grid Specification
kNN-Leiden	n_neighbors	Spread: 8, count: 5, global bounds: [3, 150]
	resolution	Spread: 0.5, count: 5, global bounds: [0.1, 5.0]
HDBSCAN	min_cluster_size	Spread: 20, count: 5, global bounds: [5, 500]
	min_samples	Spread: 10, count: 5, global bounds: [1, 100]
	cluster_selection_epsilon	Spread: 0.2, count: 5, global bounds: [0.0, 2.0]
VBGMM	n_components	Spread: 3, count: 3, global bounds: [2, 30]
	weight_concentration_prior	Fixed grid: [0.01, 0.1, 1.0]
	mean_precision_prior	Fixed grid: [0.001, 0.01, 0.1]
FINCH	n_neighbors	Spread: 10, count: 5, global bounds: [3, 100]

. The best configuration from Stage 2 is used to cluster the full fixed pool of 50,000 segments.

• Evaluation metrics

Following Contribution 6, we incorporate intrinsic clustering metrics that do not require ground-truth labels and are suitable for non-convex, arbitrary-shape clusters. The primary metrics are DBCV (density-based cluster validity), conductance (graph edge-cut quality), and modularity (community structure strength), selected for their alignment with density-based and graph-based clustering paradigms. Detailed descriptions, value ranges, and interpretation guidelines are provided in Appendix C.

Additional metrics (silhouette, Calinski–Harabasz, Davies–Bouldin) are computed, see Appendix D, but are not used for primary comparison due to their restrictive geometric assumptions. Finally, UMAP visualisations are deployed for further qualitative inspection.

• Quantitative results

Table 17. Intrinsic clustering metrics on a fixed random sample of 50,000 trajectory segments (Experiment II, Contribution 6). Higher  ↑ is better for DBCV and modularity; lower  ↓ is better for conductance. Learnt embeddings consistently outperform expert features across kNN-Leiden, FINCH, and VBGMM. Complete metric tables and additional traditional metrics are provided in Appendix D; metric properties and formulations are detailed in Appendix C.

Method	Expert Features					Learnt Embeddings
	DBCV ↑	Conductance ↓	Modularity ↑	Communities		DBCV  ↑	Conductance ↓	Modularity ↑	Communities
kNN-Leiden	$-0.791$	$0.327$	$0.875$	48		$-\mathbf{0.533}$ ↑	$\mathbf{0.186}$ ↓	$\mathbf{0.906}$ ↑	47
FINCH	$-0.907$	$0.206$	$0.671$	8		$-\mathbf{0.588}$ ↑	$\mathbf{0.205}$ ↓	$0.756$	27
HDBSCAN	$0.042$	$\mathbf{0.311}$ ↓	–	2		$\mathbf{0.112}$ ↑	$0.479$	–	3
VBGMM	$-0.742$	$0.498$	$0.419$	28		$-\mathbf{0.594}$ ↑	$\mathbf{0.193}$ ↓	$\mathbf{0.756}$ ↑	28

presents the clustering metrics and the number of detected clusters for each method–representation pair. Across kNN–Leiden, FINCH, and VBGMM, learnt embeddings consistently achieve stronger intrinsic validity than expert features, reflected in higher DBCV, improved conductance, and increased modularity. In contrast, for HDBSCANembeddings, DBCV yields a higher DBCV ($0.112$ vs. $0.042$) but poorer conductance ($0.479$ vs. $0.311$). This behaviour is expected, as HDBSCAN optimises density-based cluster stability rather than graph boundary quality; consequently, conductance is less informative for density-optimised partitions (see Appendix C for a discussion of metric–method alignment).

kNN-Leiden discovers 47–48 fine-grained communities with high modularity (>0.87), reflecting well-connected route-network structures. VBGMM identifies 28 probabilistic components with consistent ELBO across representations. HDBSCAN detects 2–3 density-separated clusters with explicit noise handling, where embeddings reveal additional density modes (3 clusters including noise) compared to expert features (2 clusters). FINCH produces 8–27 hierarchical partitions, where embeddings yield finer-grained structures (27 partitions), suggesting richer multi-scale behavioural hierarchies. Segment count distributions per cluster are visualised in Appendix E. Pairwise cluster-assignment agreement (ARI, NMI, FMI) across all four methods is reported in Appendix J; the three fully covering algorithms converge to mean NMI $=0.60$ on learnt embeddings vs. $0.37$ on expert features, confirming that the identified behavioural groupings are a robust, algorithm-independent property of the representation space.

• Interpretation and operational context alignment

Figure 8 compares the organisational structure of learnt embeddings and expert features through UMAP projections of VBGMM clustering results (28 components). The visual analysis reveals a fundamental difference in how the two representations partition maritime trajectories.

The learnt embeddings (Figure 8a) exhibit well-separated, spatially compact clusters forming distinct communities with clear boundaries and minimal overlap, as shown in the left panel coloured by cluster assignment. Critically, the ship-type overlay (right panel) demonstrates that individual clusters contain mixed vessel types—cargo, passenger, sailing, and other vessels coexist within the same behavioural community. This heterogeneity indicates that the learnt representation does not separate trajectories by vessel class, but instead organises them according to behavioural patterns that transcend vessel type. Section 7 provides SHAP analysis quantifying the specific features responsible for embedding formation and cluster assignments.

In contrast, expert features (Figure 8b) produce a diffuse clustering structure dominated by a single large central cluster (dark red/brown, left panel) with substantial inter-cluster overlap throughout the UMAP space. The ship-type overlay (right panel) reveals fundamentally different organisation: vessel types form more segregated spatial regions, with cargo vessels concentrated in the dominant central mass and passenger/sailing vessels occupying peripheral areas. This pattern suggests that expert features—comprising kinematic descriptors and spatial attributes—primarily cluster vessels by their characteristic motion profiles and physical properties rather than by operational behavioural context.

The quantitative metrics in Table 17 confirm the superior clustering structure of learnt embeddings: DBCV ($-0.594$ vs. $-0.742$), conductance ($0.193$ vs. $0.498$), and modularity ($0.756$ vs. $0.419$). This embedding-based organisation directly supports the framework’s objective (Contribution 1): by grouping trajectories according to behavioural patterns rather than vessel attributes, learnt representations enable an autonomous vessel to identify operationally similar navigation scenarios across different vessel types. For instance, a cargo vessel and a passenger ferry executing similar manoeuvring patterns would be grouped together in embedding space despite their different physical characteristics, allowing an autonomous system to learn from both examples and transfer knowledge across vessel classes. Expert features, by separating vessels primarily by kinematic and physical attributes, do not provide this cross-vessel behavioural coherence necessary for context-aware autonomous decision-making.

Figure 8 presents the representative case for VBGMM, complete UMAP projections for all clustering methods are provided in Appendix F, where similar patterns are consistently observed.

7. Discussion

This study presents a systematic evaluation of Self-Supervised Learning Representation Learning for maritime trajectory analysis through a dual-pipeline framework. Pipeline 1 employs supervised linear probing to identify the encoder architecture that yields the most discriminative latent representations for vessel-type classification, while Pipeline 2 applies unsupervised clustering to assess whether learnt embeddings naturally expose intrinsic behavioural structure aligned with operational context. The comparative evaluation benchmarks three proposed methods—GMAE-REx (semantic group masking with environment-invariant regularisation), EAE (Evidential uncertainty quantification), and DAE (reconstruction baseline)—against three established architectural baselines (Transformer, TCN, LiST). Both pipelines operate on two-year AIS dataset from the Kiel Fjord region (Contribution 1), processed through a comprehensive preprocessing pipeline that transforms raw positional broadcasts into structured trajectory representations enriched with kinematic, spatial, density, and ship-to-ship interaction features.

7.1. Encoder Selection via Supervised Probing

Experiment I follows the three-stage framework—self-supervised pretraining, linear probe, and full fine-tuning—to compare three encoders under a unified ship-type prediction task, and three baselines. This three-stage protocol identifies GMAE-REx as the optimal encoder architecture, achieving a validation accuracy of $86.03\%$ on the debiased ship-type classification task. This performance surpasses all baseline methods: DAE achieves $85.63\%$, EAE reaches $85.56\%$, the Vanilla Transformer attains $84.93\%$, LiST obtains $85.12\%$, and TCN achieves $76.27\%$.

The performance margin over the strongest baselines is modest but consistent across hyperparameter configurations, indicating that the combination of semantic feature-group masking and REx-based regularisation offers a measurable advantage over purely reconstruction- or evidential-based objectives.

The feature debiasing protocol in Pipeline 1—removing vessel dimensions and static attributes—ensures that classification performance reflects behavioural pattern learning rather than memorisation of vessel characteristics. See Section 5.

Under this constraint, the superior performance of GMAE-REx supports the hypothesis that group-wise masking encourages the model to learn cross-category relationships between temporal, kinematic, spatial, density, and interaction features, whilst REx discourages environment-specific overfitting by penalising reconstruction risk variance across traffic-density-based pseudo-environments. The gap between attention-based encoders (GMAE-REx, DAE, EAE, Transformer; $84.93$–$86.03\%$) and the convolutional TCN baseline ($76.27\%$) suggests that global temporal dependencies captured by self-attention are more informative for this probing task than local receptive fields constructed via dilated convolutions. At the same time, the competitive performance of the LiST encoder ($85.12\%$) indicates that explicit linear temporal–spatial projections can provide a viable, computationally efficient alternative when deployment conditions favour lightweight models. Based on these results, GMAE-REx is selected as the final encoder $(E^{\star },{\theta }^{\star })$ and used in Pipeline 2 for unsupervised structural analysis.

7.2. Intrinsic Structure of Learnt Embeddings

Experiment II compares the intrinsic clustering structure of GMAE-REx embeddings with that of an expert-selected nautical feature set across four clustering backends. On a fixed pool of 50,000 segments, embeddings consistently outperform expert features for kNN–Leiden, FINCH, and VBGMM across the primary intrinsic metrics DBCV, conductance, and modularity (Table 17).

For kNN–Leiden, DBCV improves from $-0.791$ (expert) to $-0.533$ (embeddings), conductance decreases from $0.327$ to $0.186$, and modularity increases from $0.875$ to $0.906$, indicating denser communities with cleaner graph cuts and stronger community structure in the embedding space.

For FINCH, embeddings increase DBCV from $-0.907$ to $-0.588$ and modularity from $0.671$ to $0.756$, whilst the number of communities rises from 8 to 27, revealing finer-grained multi-scale structure.

For VBGMM, embeddings improve DBCV from $-0.742$ to $-0.594$, reduce conductance from $0.498$ to $0.193$, and raise modularity from $0.419$ to $0.756$ with the same number of components (28), suggesting a more coherent probabilistic partition.

HDBSCAN displays a different pattern: embeddings yield higher DBCV ($0.112$ vs. $0.042$) but worse conductance ($0.479$ vs. $0.311$) relative to expert features. This behaviour is consistent with HDBSCAN’s optimisation objective, which favours density-based cluster stability and explicit noise identification rather than graph boundary quality; conductance is therefore less informative for assessing HDBSCAN partitions.

Taken together, these results indicate that the latent space learnt by GMAE-REx better captures density-connected and community-structured organisation of trajectories than the expert-crafted representation, especially under graph- and mixture-based clustering methods. For instance, considering UMAP visualisations of VBGMM components clarifies how embeddings differ from expert features (Figure 8). In the embedding space, 28 components form compact and well-separated clusters with clear boundaries, where each cluster contains mixed ship types (cargo, passenger, sailing, other), indicating organisation by operational navigation modes that transcend vessel class. In contrast, the expert feature space exhibits a dominant central cluster with substantial overlap between components and stronger ship-type segregation, suggesting that clustering primarily follows kinematic and physical similarities (e.g., typical speed profiles per vessel class). This behaviour-centric organisation in the embedding space is advantageous for MASS, as it facilitates recognition of similar navigation scenarios across heterogeneous vessel types.

7.3. Feature-Based Analysis: Operational Context Alignment

Feature-based analysis provides additional evidence that the discovered structure is behaviour-relevant rather than arbitrary. When the embedding space is coloured by trajectory-level mean values of contextual and physical variables (Figure 9), distinct regions align with interpretable factors such as vessel size, water depth, distance to land, and distance to restricted areas.

Cargo trajectories concentrate in two dominant regions on the left side of the embedding space (Figure 9a). Both regions are associated with larger vessel length (Figure 9b) and width (Figure 9c), while they differ systematically in operating context. One region aligns with deeper waters (Figure 9d) and larger distances to land (Figure 9e) and restricted areas (Figure 9f), whilst the other region aligns with shallower waters and closer proximity to coastlines and regulated regions. Passenger and sailing trajectories appear more frequently in other regions (Figure 10) and are associated with smaller vessel dimensions and different distance-to-land patterns. Passenger trajectories (Figure 10b) occur closer to land, consistent with ferry operations in confined port waters, while sailing trajectories (Figure 10c) are more common in central regions farther from the coastline.

These patterns support the interpretation that the embedding space captures meaningful operational context and behaviour-related conditions rather than vessel identity alone.

7.4. Explainability of Cluster Structure via SHAP

To understand which input features drive the cluster structure in embedding space, we apply Kernel SHapley Additive exPlanations (SHAP) analysis to the VBGMM assignments (28 components) on learnt embeddings. SHAP values quantify the marginal contribution of each feature to cluster assignments, providing a principled explainability framework grounded in cooperative game theory. VBGMM is selected as the primary example for detailed discussion due to its probabilistic partition structure and balanced cluster sizes; complete SHAP analyses for kNN-Leiden, FINCH, and HDBSCAN, including per-cluster feature attributions and sensitivity studies, are provided in Appendix H.

7.4.1. Global Feature Importance

Global SHAP values aggregated across all 28 VBGMM clusters reveal that temporal encodings dominate the ranking (Figure 11): day_of_year_cos and day_of_year_sin exhibit the highest mean absolute importance, followed by day_of_week_cos and day_of_week_sin.

This temporal dominance suggests that seasonal and weekly patterns—such as summer ferry traffic versus winter shipping schedules, or weekday commercial operations versus weekend recreational activity—are primary drivers of behavioural variation in the Kiel Fjord dataset. Kinematic features occupy mid-range positions (length, speed, course_cos, course_sin, acc), whilst environmental features (water_depth, dist_to_land, density_all, density_own_group, dist_to_ferry_route) occupy mid-to-lower ranks. Vessel attributes (width, ship_type) and interaction features (dcpa_0, tcpa_0, collision_risk_0) contribute at moderate levels.

This hierarchy indicates that whilst static vessel characteristics and spatial context inform cluster structure, they are not primary differentiators, consistent with the hypothesis that operational context, not vessel identity, defines behavioural modes. Global SHAP rankings for kNN-Leiden, FINCH, and HDBSCAN are provided in Appendix G.

7.4.2. Per-Cluster Feature Importance

Per-cluster SHAP rankings reveal heterogeneous feature dependencies across behavioural modes (Figure 12). Whilst temporal features remain consistently important across most clusters, specific clusters exhibit elevated importance for kinematic, environmental, or interaction features. For example, Cluster 0 ($n=2397$, the largest cluster) shows temporal features in top positions, followed by rel_bearing_1_cos, course_sin, and dist_to_land, suggesting a high-traffic transit cluster with mixed vessel sizes operating under typical seasonal conditions. Cluster 1 ($n=2$, an outlier cluster) exhibits strong importance for rel_bearing_1_cos, course_sin, and course_diff_1_cos, indicating trajectories characterised by specific interaction geometries and directional consistency, potentially corresponding to close-quarters encounters or special manoeuvres. Cluster 2 ($n=10$) prioritises course_sin, dist_to_restricted_area, and rel_bearing_1_cos, suggesting navigation near regulated zones with specific heading constraints.

The diversity of per-cluster SHAP rankings indicates that GMAE-REx embeddings encode multi-faceted behavioural representations where different feature categories become salient depending on operational context, rather than relying on a single dominant signal. Complete per-cluster SHAP rankings for all 28 VBGMM clusters, as well as per-cluster analyses for kNN-Leiden (48 clusters), FINCH (27 clusters), and HDBSCAN (3 clusters), are detailed in Appendix H.

7.4.3. Cluster Centroid Profile Interpretation

Cluster centroid profiles visualise normalised mean feature values across seven key maritime dimensions—water depth, distance to land, speed, distance to restricted areas, vessel width, vessel length, and traffic density—providing intuitive geometric representations of each cluster’s characteristic operational signature (Figure 13). For each cluster, feature values are aggregated as means across all member trajectories, then normalised to [0,1] relative to the global minimum and maximum observed across all clusters within the method, enabling direct visual comparison of operational contexts.

Clusters with large polygons spanning most axes (e.g., Cluster 7, $n=40$) indicate trajectories with consistently high normalised values across multiple dimensions, potentially representing large vessels operating in confined, high-traffic waters near restricted areas. Clusters with balanced mid-range profiles (e.g., Cluster 10, $n=162$) suggest typical open-water transit conditions with moderate values across all features. Clusters with irregular, spike-shaped profiles (e.g., Cluster 1, $n=2$) reveal specialisation along specific dimensions—such as elevated water depth combined with low traffic density and specific distance-to-land characteristics—consistent with offshore navigation or outlier manoeuvres.

The diversity of radar profile geometries across 28 clusters underscores the embedding’s capacity to capture fine-grained operational nuances beyond coarse vessel-type categories. These centroid visualisations complement the SHAP feature attribution analysis (Figure 11 and Figure 12) by translating cluster centroids into interpretable geometric signatures: whilst SHAP quantifies which features drive cluster assignments, centroid profiles reveal what values those features take within each cluster, enabling domain experts to validate clustering outputs against known maritime operational categories. Individual cluster profiles and cross-method comparisons for kNN-Leiden (47 clusters), FINCH (27 clusters), and HDBSCAN (3 clusters) are detailed in Appendix I.

7.5. Metric Interpretation and Granularity

The absolute values of intrinsic metrics highlight the difficulty of unsupervised behaviour discovery for maritime trajectories. DBCV remains negative for both representations across kNN-Leiden, FINCH, and VBGMM (Table 17), which is consistent with a continuous spectrum of behaviours rather than well-separated, compact clusters.

The consistent gains in DBCV, conductance and modularity indicate that the learnt embeddings provide a better geometric and graph structure for community discovery, even when behaviours remain partially continuous.

Community detection also involves a granularity trade-off. A partition with more communities is not automatically better; a useful representation is expected to support communities that are coherent, well separated in the graph, and stable under intrinsic criteria. The embedding-induced communities achieve higher modularity and lower conductance together with comparable or fewer communities (kNN-Leiden: 47 vs. 48; VBGMM: 28 vs. 28; FINCH: 27 vs. 8), which is consistent with a more structured partition rather than a fragmented one.

7.6. Comparison with Expert-Engineered Features

Including expert-designed nautical features (SOG, COG, turn rate, proximity to infrastructure, vessel dimensions) as a baseline clarifies what is gained by self-supervised representation learning. For graph-based and mixture models, embeddings consistently achieve higher DBCV and modularity and lower conductance than expert features (Table 17), with relative improvements of $32.6\%$ for kNN-Leiden DBCV, $35.2\%$ for FINCH DBCV, and $19.9\%$ for VBGMM DBCV, indicating more compact and better-separated communities in the embedding space.

The expert feature space retains interpretability advantages for domain practitioners: a nautical expert can directly verify whether a trajectory segment exhibits high SOG or sharp turns, whereas latent embedding dimensions lack direct physical meaning. However, the UMAP projections (Figure 8, Appendix F), feature-mean visualisations (Figure 9 and Figure 10), and intrinsic metrics (Table 17, Appendix D) demonstrate that expert features emphasise vessel-class-specific motion envelopes rather than context-dependent behaviours that generalise across classes. This implies a trade-off: embedding-based clustering better supports tasks that require recognition of similar scenarios across heterogeneous vessels (e.g., identifying congested, shallow-water manoeuvring irrespective of ship type), whereas expert features may be preferable when the primary goal is to diagnose class-specific performance or to communicate results to practitioners using directly interpretable quantities. Hybrid approaches that combine learnt embeddings with a small set of high-level nautical descriptors could offer a promising compromise between structural quality and human interpretability.

7.7. Labels and Vessel-Type Alignment

The community structure is not expected to align perfectly with vessel-type labels. Vessel type is largely static, while navigation behaviour is context-driven and dynamic. Different vessel types can adopt similar manoeuvring strategies under the same encounter geometry and fairway constraints, as evidenced by the mixed-type composition of individual clusters in Figure 8. The same vessel type can also exhibit different behaviours across operational states such as transit, waiting, berthing, and service operations.

In a fully unsupervised setting, vessel type is therefore more appropriate as a post-hoc attribute for interpretation than as a target that must be separated. This design choice aligns with the framework’s objective (Contribution 1): by grouping trajectories according to behavioural patterns rather than vessel attributes, learnt representations enable an autonomous vessel to identify operationally similar navigation scenarios across different vessel types, facilitating cross-vessel knowledge transfer for context-aware autonomous decision-making.

7.8. Cluster-Level Collision Risk Case Studies

The collision risk index (Equation (1)) combines TCPA and DCPA into a single safety-relevant scalar that fires only when both conditions hold simultaneously: a vessel must be on an imminent intercept track (low TCPA) and projected to pass with dangerously small separation (low DCPA). Neither quantity alone is sufficient: a low TCPA with a large DCPA describes parallel traffic that resolves safely; a large TCPA with a small DCPA indicates a future near-miss that current separation will prevent. The composite index therefore provides a more reliable operationalisation of collision exposure than either component in isolation. To link discovered clusters to concrete navigational scenarios, Figure 14 visualises the spatial collision risk profiles for two contrasting kNN-Leiden behavioural clusters. For each cluster, the Kiel Fjord bounding box is rasterised at $10\mathrm{m}\times 10\mathrm{m}$ resolution, and each cell is coloured by the mean collision risk (Equation (1)) averaged over all AIS observations from trajectories belonging to that cluster. This produces a geographic heat map of where vessels in a given behavioural group characteristically experience high or low encounter danger.

Cluster 16—high-risk encounter pattern. The spatial profile of Cluster 16 (Figure 14a) shows elevated mean collision risk concentrated in the central navigational channel and around the ferry-terminal approach of Kiel Fjord. These are the geometrically constrained zones where converging vessel tracks naturally produce small DCPA values simultaneously with short TCPA, corresponding to vessels that cannot deviate to increase separation. The cluster therefore captures a distinct behavioural mode: trajectory segments in which the ego vessel is consistently operating in close-quarters situations, regardless of vessel type or speed class. This is consistent with the SHAP analysis (Section 7.4), which identifies interaction features (collision_risk_0, dcpa_0, tcpa_0) as non-trivially contributing features in clusters with elevated encounter density.

Cluster 29—low-risk transit pattern. In contrast, the spatial profile of Cluster 29 (Figure 14b) shows near-zero mean collision risk across the entire Kiel Fjord area. The near-uniform low-risk colouration indicates that trajectory segments in this cluster consistently encounter other vessels either at large spatial separations or with ample temporal margin before closest approach—conditions characteristic of open-water transit or well-separated route following. The geographic spread of non-zero cells confirms that this is not a spatially trivial cluster (e.g., vessels exclusively in peripheral areas with no traffic), but rather a genuine behavioural class defined by how vessels interact with surrounding traffic, not merely by where they happen to be located.

Taken together, these two profiles demonstrate that the kNN-Leiden clusters discovered from GMAE-REx embeddings correspond to verifiable, safety-relevant navigational scenarios. The collision risk spatial maps provide a direct, chart-level validation criterion: if a cluster genuinely represents a cognitively distinct behavioural mode, its mean collision risk surface should show a coherent geographic pattern, not random noise distributed uniformly across the study area. The contrast between Cluster 16 and Cluster 29 confirms this hypothesis, supporting the operational validity of the learnt representation space for maritime situational awareness and risk-screening applications.

7.9. Practical Implications for Maritime Autonomous Systems

The representation and community structure obtained in this work enable several practical applications in maritime systems:

• Vessel Traffic Services (VTS): Online trajectories can be mapped into the learnt embedding space and compared against community prototypes for behaviour recognition and monitoring. Dominant communities provide baselines for expected-route modelling and traffic-flow analysis, while deviations from typical community regions can be used as indicators of unusual behaviour and for early-stage risk screening.
• Maritime Autonomous Surface Ships (MASS): A stable and generalisable representation can serve as input to decision-making and risk-assessment modules, reducing reliance on handcrafted features. The embedding also supports label-efficient behaviour modelling via transfer learning, which is particularly valuable under limited supervision.
• Safety Analysis and Simulation: Community structure supports systematic scenario organisation by grouping trajectories with similar operational context, facilitating structured coverage of operational design domains for simulation, testing, and validation.

Offline preprocessing latency was estimated at ≈811 ms per 10 min segment on a single CPU core (see Appendix K for full experimental details), confirming that the per-unit throughput of the pipeline is well within the 10 min update cadence of MASS situational awareness.

8. Conclusions

This section concludes the paper by summarising the main findings and contributions of this work. It also outlines several directions for future research, building on the proposed representation learning framework.

8.1. Summary

This work focuses on the core problem of robust behavioural representation learning from maritime AIS trajectory data. It systematically investigates how to construct representations that can generalise across environments and provide interpretability in maritime scenarios characterised by strong environmental heterogeneity, limited labels, and high safety requirements. To address the limitations of existing methods in environment generalisation, feature structure utilisation, and uncertainty modelling, this paper proposes and validates a complete self-supervised representation learning framework.

First, we develop a comprehensive AIS data processing and feature modelling pipeline that transforms raw, sparse, and noisy vessel broadcast data into structured trajectory representations with multiple semantic layers, including temporal, kinematic, spatial, traffic density, and ship-to-ship interaction information. This pipeline provides a solid foundation for subsequent representation learning and offers a reusable data engineering paradigm for maritime trajectory analysis.

At the methodological level, we propose the GMAE-REx representation learning model. By introducing structured masking at the level of semantic feature groups, the model is explicitly encouraged to learn cross-category relationships between different feature types. In addition, we integrate REx regularisation from the domain generalisation literature into the self-supervised reconstruction objective, effectively reducing overfitting to specific traffic densities or geographical conditions. For comparison, we also systematically evaluate a denoising autoencoder (DAE) and an uncertainty-aware evidential autoencoder (EAE), enabling a unified assessment of different self-supervised strategies for maritime trajectory modelling.

For evaluation, we design a dual-pipeline experimental framework. On the one hand, a frozen-encoder classification task is used to objectively assess the discriminative power of the learned representations on a downstream vessel-type classification task. On the other hand, multiple unsupervised clustering methods are applied to analyse the intrinsic structure of the representation space. Experimental results show that GMAE-REx achieves stable and consistent performance advantages in the vessel classification task, demonstrating its ability to effectively capture vessel behaviour patterns. At the same time, in unsupervised clustering, the learned embeddings significantly outperform expert-engineered features across multiple intrinsic metrics, and the resulting cluster structures reflect operational context and behavioural modes rather than static vessel-type differences.

Furthermore, by combining UMAP visualisation, feature mean analysis, and SHAP-based explainability, this work systematically reveals the physical meaning of different behavioural clusters in the embedding space. The results show that temporal patterns, kinematic states, environmental constraints, and interaction geometry exhibit different levels of importance across clusters, confirming the interpretability of the learned representations and their ability to integrate multiple feature modalities. This behaviour-oriented organisation of trajectories, rather than vessel-type-based separation, supports knowledge transfer and scenario understanding across heterogeneous vessel classes.

From an application perspective, the proposed representation learning and community discovery framework provides a general and scalable foundation for behaviour monitoring in VTS, decision support for MASS, and maritime safety analysis.

8.2. Future Work

Although this work achieves systematic progress in robust maritime behavioural representation learning, several directions remain open for further research.

First, vessel-type classification is mainly used in this work as a supervised probe task to validate the discriminative quality of the learned representations under a debiased setting. However, vessel classification is only one of many possible downstream tasks, and its role here is primarily to provide a standard and reproducible evaluation of representation quality. The robust trajectory representations learned in this study are naturally applicable to a wider range of maritime tasks, such as collision risk detection, abnormal behaviour identification, trajectory prediction, and remaining navigation risk assessment. Future work can systematically evaluate the generalisation and practical value of the proposed representations across these diverse task settings.

Second, although rich ship-to-ship interaction features (e.g., TCPA, DCPA, relative bearing, and collision risk indicators) are explicitly constructed during feature modelling, the current representation learning framework still follows a single-trajectory-centred encoding paradigm. This data characteristic is well aligned with graph-based modelling, where vessels can be naturally represented as nodes and their spatial proximity and interaction dynamics as time-varying edges. Future research may combine the proposed robust self-supervised learning principles with graph neural networks to directly learn interaction-aware trajectory representations from spatio-temporal vessel graphs, enabling a deeper understanding of multi-vessel coordination and collective traffic behaviour.

Third, although the clustering analysis in Experiment II reveals that GMAE-REx embeddings exhibit stronger and more consistent inter-algorithm agreement than expert features (mean NMI $0.60$ vs. $0.37$; see Appendix J), the clustering component was deliberately treated as an off-the-shelf exploratory probe whose purpose is to reveal the intrinsic structure of the representation space, not to optimise partition quality in its own right. Future work may investigate deep clustering methods—such as Deep Embedded Clustering [72] or its improved variant IDEC [73]—that co-optimise representation learning and cluster assignment simultaneously, potentially yielding sharper behavioural segmentation for the AIS domain and enabling principled anomaly detection by scoring trajectory segments against learned normal-behaviour cluster structures [13]. Such an investigation would additionally allow a principled comparison against trajectory-distance baselines (e.g., Dynamic Time Warping) on a curated representative subset, which was out of scope here due to the $\mathcal{O}\left(N^2\right)$ cost of pairwise distance computation at $N=\mathrm{50,000}$ segments.

Fourth, the preprocessing pipeline, feature engineering layer, and SSL training procedure are designed to be region-agnostic and use-case-agnostic. Every feature is derived from physical or geometric quantities—kinematic states computed from position sequences, CPA geometry, bathymetric depth, and distance to navigational structures—none of which carry location-specific encodings. The data requirements reduce to three inputs: decoded AIS broadcasts, standard nautical geo-map layers for the study area (bathymetry, land mask, ferry routes, restricted areas) that are globally available from public sources such as EMODnet and OpenSeaMap, and a vessel registry or equivalent web service (e.g., MyShipTracking, Equasis) to complete missing static vessel attributes (ship_type, dimensions) for MMSI identifiers whose static AIS reports are absent or incomplete. The CPA calculator for ship-to-ship interaction features is already integrated into the preprocessing pipeline. Applying the pipeline to a new maritime region therefore reduces to supplying the corresponding AIS archive and raster layers, and re-running the SSL training on the new data. A natural next step is to instantiate the framework on AIS archives from complementary environments—such as open-sea shipping lanes, bulk-cargo ports, or coastal archipelagos with different vessel-type mixes and fairway topologies—and compare the resulting community structures across regions, both to assess the generality of the discovered behavioural patterns and to study how environmental geometry shapes vessel behaviour.

8.3. Limitations

The experimental evaluation relies on a single temporal split (approximately 70% training, 20% validation, and 10% test, chronologically ordered within the 2022–2023 Kiel Fjord dataset). While this split reflects realistic temporal deployment conditions and avoids data leakage, it does not yield multi-seed or cross-validation confidence intervals for the linear probe accuracy values reported in Table 12. Performing repeated self-supervised learning pre-training across multiple seeds or folds is computationally prohibitive at this dataset scale: with 527,225 training segments of $L=120$ timesteps each, a single GMAE-REx pre-training run requires substantial GPU compute, and replicating this across even two seeds would double the already considerable training cost.

Notwithstanding this constraint, the absolute size of the evaluation set provides substantial intrinsic statistical reliability. Our held-out test partition alone comprises approximately 52,722 trajectory segments from 9948 unique vessels spanning two years of recorded maritime traffic. For context, this figure substantially exceeds the complete training corpora reported in comparable maritime AIS trajectory learning studies [39,40,74], suggesting that performance estimates derived from this large held-out set are inherently more stable than those from smaller benchmarks in the field.

The cluster analysis in Experiment II uses standard off-the-shelf algorithms as an exploratory tool to probe the geometric structure of the learnt representation space. The algorithms were selected for diversity of inductive bias (graph modularity, Bayesian mixture, hierarchical first-neighbour, density-based), not jointly optimised for maximal partition quality. Accordingly, the absolute clustering metrics (silhouette coefficient, DBCV, and mutual-information scores) should be interpreted as indicative rather than as upper bounds. The consistent advantage of learnt embeddings over expert features across all methods and metrics provides strong evidence for the quality of the representation, and pairwise inter-algorithm agreement (mean NMI $=0.60$ on embeddings vs. $0.37$ on expert features) confirms that the recovered structure is a genuine, algorithm-independent property of the space (Appendix J). The question of whether jointly trained deep-clustering objectives can further sharpen this structure is left to future work.