# Trajectory Mining and Routing: A Cross-Sectoral Approach

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## Abstract

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## 1. Introduction

- The exploitability of AIS data in path planning and weather routing applications is limited. Therefore, this research builds on the exploitation of past vessel trajectories derived from AIS data and develops a fine-tuned grid of possible vessel routes.
- The development of an A* search algorithm for optimal path planning based on the historical vessel routes.

## 2. Related Work

**Classification**From the early work on TraClass [21] that introduced the concept of trajectory partitioning, then applied clustering to trajectory segments to the more recent works on movelets [24], the process is almost always similar: (i) partition the trajectory into subtrajectories of either equal length or duration or based on changes in the trajectory properties, (ii) define a similarity or distance measure for comparison of subtrajectories that are considered the features that describe each trajectory, and (iii) expand this measure to calculate the similarity between a prototype trajectory (i.e., class representative) and all other trajectories. In a similar line, the authors of [25] proposed a shapelet-based [26] classification framework for the detection of specific search-and-rescue maneuvers performed by vessels. They employed a genetic algorithm to find the best shapelets to use as features and managed to significantly reduce the complexity of their approach without a significant loss in terms of accuracy. More recent approaches attempt to classify the trajectory as a whole, either extracting features from the distributions of speed, longitude, latitude, and course in the whole trajectory [27] or by examining the trajectories as images [28,29] and applying popular classification algorithms to them (from random forests to CNNs). In this line, the authors of [30] employed a segmentation and clustering approach to identify different types of travel patterns, such as regular commuting, leisure travel, and airport transportation based on data on ride-hailing passengers.

**Clustering**techniques are the most popular in trajectory mining since they allow for the creation of meaningful groups of trajectories or trajectory segments that share the same location, shape, or movement characteristics. TraClus [31], the first trajectory clustering algorithm, is based on a partition-and-group approach and a composite distance function for trajectory segments and combines the perpendicular, parallel, and angle distances. DBSCAN is a basic algorithm that was extended to capture the composite distance function. In [32], DBSCAN was incorporated into a holistic, modular framework (TREAD) that identifies vessel traffic patterns in real time to realize an informed decision-making procedure through causal analysis and pattern recognition. The authors of [33] were able to associate vessel types (containers, Ro-Ro, etc.) with route segments by utilizing geometry-based fuzzy membership functions. More recently, the authors of [34] presented another extended version of DBSCAN that, apart from the locational and directional features of the moving object, also considers its speed in an attempt to create clusters in which the objects move close to each other, almost in parallel, and with similar speeds. The authors of [35] conducted a comprehensive survey of trajectory clustering techniques, including spatial and time-dependent clustering, partition and group clustering, and semantic trajectory clustering. They also summarized the main distance and similarity measures that are used by the algorithms.

**Outlier and anomaly detection**techniques usually rely on clustering or classification in the first step in order to find the trajectories that lack a corresponding match within the dataset. The applications vary from object tracing to climate monitoring and road network management, and apart from classification and clustering, statistic-based and density-based techniques are also employed to find samples that diverge from the normal distribution [36,37]. Once again, a representation of the trajectory or subtrajectory in the first step and a distance or similarity measure in the second step are needed to group similar items together and detect outliers. The anomaly detection framework proposed in [38] provides a different approach that combines a maritime trajectory model as a basis comprising moving objects’ trajectory streams with a grid partitioning of the space to discover infrequent regions that contain outlying trajectory segments or segments that diverge from the main streams. In [39], a complex event recognition framework was introduced, utilizing event calculus for real-time outlier detection in AIS data streams corresponding to vessel trajectories.

**Graph-based**techniques have frequently been employed to trajectory data, especially in the transportation domain. Authors usually represent the movement trends of the monitored entities on a graph that contains POIs, entities (i.e., persons, vehicles, or vessels) as nodes, and their connectivity across spatiotemporal and semantic dimensions as edges in order to create a network or graph abstraction. Then they perform queries that extract frequent patterns from the graph. In [40], the authors exploited historical data of vessel trajectories in order to understand maritime routes and traffic. In the same context, the authors of [41] presented a methodology for extracting the navigation network of an area from AIS data. The nodes in the final graph represent points of interest with respect to the vessel trajectories, such as ports or points of major change in speed and direction (waypoints), and the edges are the result of the clustering of trajectory segments from multiple vessels. The segments share similar location, direction, and speed properties. In a slightly different approach, the authors of [42] employed a graph-based spatiotemporal convolutional network trained on past vehicle trajectories to predict vehicle trajectories in an autonomous driving scenario. The vehicles were considered the nodes of the graph, and their past trajectories were encoded as node features. The graph was fully connected, but the edges’ weights model the effect that each vehicle has on surrounding vehicles. The proposed approach allows for the simultaneous prediction of the future location of all vehicles at once.

**Trajectory prediction**is one of the most prominent tasks, with many applications in tourism, transportation, traffic management, etc. The comprehensive survey of human trajectory prediction reported in [43], the surveys of machine learning approaches for vehicle trajectory prediction presented in [44,45], and the recent survey of vessel trajectory prediction techniques [46,47] all agree that either physics- (turn rate, velocity, and acceleration) or statistics-based methods (Kalman filters and Monte Carlo methods) can be employed to predict the future position of a moving object, and they propose the use of deep learning techniques to implicitly capture the complex dynamics of motion, especially in the context of other moving objects, in order to predict the evolution of a trajectory. In [48], the authors proposed a transformer-based context-aware network that captures POI visiting sequences from trajectories, enriches them with semantic and social context, and predicts the next POI to be visited in an ongoing trajectory. Similarly, the authors of [49] proposed a spatiotemporal LSTM network that processes semantic trajectories from Foursquare and predicts the future locations of persons moving around a city. These works go beyond the traditional spatiotemporal representation of trajectories and capitalize on multiaspect semantic trajectories [50], which, in turn, creates new research opportunities in the trajectory mining domain.

**maritime sector**, trajectory mining techniques have been adopted recently to analyze vessel movements and improve vessel safety and efficiency. In [51], TM was used to analyze vessel movements in a port. The study used trajectory clustering to identify vessel behavior patterns, such as berthing, departure, and maneuvering. The results can be used to optimize port management and improve vessel safety. Another study [52] involved the application of trajectory mining to analyze the movement patterns of fishing vessels. The study used trajectory segmentation and clustering to identify different types of fishing behavior, such as trolling, drifting, and anchoring. The results can be used to improve fishing management and reduce overfishing.

## 3. Data Overview and Processing

**Step 1.**The first step is the extraction of waypoints. Waypoints are defined as regions at sea where vessels stop completely, indicating ports or anchorage areas. By identifying such areas, the origin and destination points of a vessel can be determined. To detect such points, the AIS positions with zero speed are kept. Then, the DBSCAN algorithm is employed to cluster together positions of high density close to each other and remove any possible outliers, e.g., single positions with zero speed farther away from the ports or anchorage areas that may have been produced due to GPS errors. Empirical experiments indicated that a value of $eps$ = 2 km (an average radius of medium-sized ports) and a value of $minPts=10$ yield the best results when compared to the port database of the World Port Index1 (WPI). It is worth noting that the WPI does not contain information about anchorage areas; therefore, a unified method for identifying both ports and anchorage areas is required. Next, the resulting clusters are converted to convex hulls (the minimum bounding geometry that contains all positions of a cluster), and the final convex hulls are used as waypoints.

**Step 2.**The next step is the identification of the routes. In this step, we simply segment the trajectories of the vessels based on the waypoints to incorporate the origin–destination ports in the dataset. The result of this step is subtrajectories that start and end at a waypoint.

**Step 3.**The third step consists of interpolation of the AIS positions of each trajectory. The reason for this step is to fill the gaps that may arise in real vessel trajectories. Such gaps may affect the quality of the traffic patterns extracted with the proposed methodology, since they directly affect the quality of the clustering step that follows (Step 4). It is quite common to have such gaps in vessel trajectories because although vessels must carry an AIS transponder, the transponder does not need to be switched on [15]. This is a common tactic when vessels want to hide their tracks and conceal their whereabouts to avoid piracy attacks or perform an illegal act themselves (e.g., fishing in prohibited areas). AIS gaps in trajectories may also happen either due to poor weather condition; because the receivers are deliberately jammed; or, on rare occasions, because of packet collisions that take place when the AIS receivers are flooded with messages. To this end, Lagrange interpolation, a well-known and established algorithm was employed for each trajectory, which is preferred over Newton interpolation because it provides more accurate approximations. The interpolation itself is not the focus of our study; nevertheless, the various interpolation techniques can be used in the future to further study their effects on our approach.

**Step 4.**The fourth and final step is trajectory clustering. In this step, a modified iteration of the DBSCAN algorithm was utilized to cluster trajectories involving multiple vessels following the same route (from waypoint to waypoint). This clustering was based on various factors, including the geographical location, speed, and heading of the AIS positions. Specifically, the surveillance area was segmented into a grid with a resolution of ${0.2}^{\circ}$—a resolution that matches the Copernicus Climate Change Service2 (C3S) and can be utilized in future studies to find optimal route recommendations. In each grid cell, the standard deviations of speed over ground, course over ground, and distance between AIS positions were calculated. We used the standard deviation because it measures the amount of variation or dispersion of a set of values. Positions with the lowest dispersions of speed, heading, and Haversine distance need to be grouped together. Then, a modified DBSCAN algorithm is employed to further cluster the AIS positions of each vessel type and origin–destination waypoints in each grid cell. The modified DBSCAN algorithm employs two more parameters other in addition to the $eps$ and $minPts$ parameters, which remain the same: the s and c parameters, refer to the speed and the course over ground, respectively. The values of s and c used for the clustering are the previously calculated standard deviation values of speed and course over ground for each grid cell. $eps$ is the standard deviation of the distance. $minPts$ is set to 6 because we need at least two three-position-length routes per itinerary. Three is the minimum number of positions a trajectory should have to be considered valid. Therefore, clusters with one route are not considered common and are excluded from the process. Then, the convex hulls per cluster are calculated. Consequently, numerous polygons emerged along each route, with each polygon representing the specific area where vessels operated with similar speeds and headings. An illustration of such polygons is depicted in Figure 3. More details about the preprcessing steps can be found in [34,41].

## 4. Trajectory Mining and Ocean Path Planning

#### 4.1. Derivation of AIS Clusters Based on Shortest-Path Principles

**A***algorithm, to extract a rough approximation of the shortest path between our origin and the destination.

Algorithm 1 Algorithm for AIS cluster extraction based on a path. |

Require: shortest path from A*${\mathcal{S}}_{\mathit{P}}\leftarrow $ A* based on sea gridRequire: Convex Hull of clusters ${\mathcal{C}}_{\mathit{H}}\leftarrow $ from initial processingRequire: Centroids ${\mathcal{C}}_{\mathit{i}}\leftarrow $ from ${\mathit{C}}_{\mathit{H}}$Require: candidate AIS clusters list
${\mathcal{C}}_{\mathit{l}}$1: for each ${\mathit{w}}_{\mathit{i}}\in {\mathcal{S}}_{\mathit{P}}$ do2: for each ${\mathit{c}}_{\mathit{i}}\in {\mathcal{C}}_{\mathcal{H}}$ do3: if $\mathcal{D}\mathit{i}\mathit{s}{\mathit{t}}_{\mathit{g}\mathit{e}\mathit{o}\mathit{d}\mathit{e}\mathit{s}\mathit{i}\mathit{c}}({\mathit{w}}_{\mathit{i}},{\mathit{c}}_{\mathit{i}})<\mathit{d}\mathit{i}\mathit{s}\mathit{t}$ then4: if $\mathit{s}\mathit{p}\mathit{e}\mathit{e}\mathit{d}\left[{\mathit{w}}_{\mathit{i}}\right]>10$ then5: add ${\mathit{w}}_{\mathit{i}}$ to ${\mathcal{C}}_{\mathit{l}}$ 6: Return ${\mathcal{C}}_{\mathit{l}}$ |

#### 4.2. Building the Custom Grid

Algorithm 2 Algorithm for grid construction. |

Require: Convex Hull of filtered clusters ${\mathcal{C}}_{{\mathit{H}}_{\mathit{f}}}\leftarrow $ from initial processingRequire: Rectangle defining bounding box for selected voyage←$\mathit{m}\mathit{i}{\mathit{n}}_{\mathit{l}\mathit{o}\mathit{n}},\mathit{m}\mathit{a}{\mathit{x}}_{\mathit{l}\mathit{o}\mathit{n}},\mathit{m}\mathit{i}{\mathit{n}}_{\mathit{l}\mathit{a}\mathit{t}},\mathit{m}\mathit{a}{\mathit{x}}_{\mathit{l}\mathit{a}\mathit{t}}$ 1: for each $\mathit{l}\mathit{o}{\mathit{n}}_{\mathit{i}}$$\in [\mathit{m}\mathit{i}{\mathit{n}}_{\mathit{l}\mathit{o}\mathit{n}},\mathit{m}\mathit{a}{\mathit{x}}_{\mathit{l}\mathit{o}\mathit{n}}]$ with step 0.1 do2: for each $\mathit{l}\mathit{a}{\mathit{t}}_{\mathit{i}}$$\in [\mathit{m}\mathit{i}{\mathit{n}}_{\mathit{l}\mathit{a}\mathit{t}},\mathit{m}\mathit{a}{\mathit{x}}_{\mathit{l}\mathit{a}\mathit{t}}]$ with step 0.1 do3: if ($\mathit{l}\mathit{a}{\mathit{t}}_{\mathit{i}}$, $\mathit{l}\mathit{o}{\mathit{n}}_{\mathit{i}}$) ∈ ${\mathcal{C}}_{\mathit{H}}{}_{\mathit{f}}$ then4: add ($\mathit{l}\mathit{a}{\mathit{t}}_{\mathit{i}}$, $\mathit{l}\mathit{o}{\mathit{n}}_{\mathit{i}}$) to ${\mathcal{G}}_{\mathit{s}}$ 5: Return ${\mathcal{G}}_{\mathit{s}}$ |

#### 4.3. Shortest-Path Planning Based on Tailor-Made Employed Grid

## 5. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | https://msi.nga.mil/Publications/WPI, accessed on 2 January 2024. |

2 | https://climate.copernicus.eu/, accessed on 2 January 2024. |

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**Figure 10.**Alternative route construction. (

**a**) Extracted AIS shortest path for the VENEZIA–PIRAEUS voyage. (

**b**) Clusters assigned to waypoints of alternative route segments.

**Figure 11.**Alternative route construction. (

**a**) Marseille–Piraeus. (

**b**) Barcelona–Piraeus. (

**c**) Alexandria–Barcelona.

Basic Comparison | A to B via C | AIS Routing |
---|---|---|

Distance (nm) (a) | 1133.4 | 1100.36 |

Distance (nm) (b) | 1182.9 | 1163.43 |

Distance (nm) (c) | 1483.49 | 1474.99 |

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## Share and Cite

**MDPI and ACS Style**

Kaklis, D.; Kontopoulos, I.; Varlamis, I.; Emiris, I.Z.; Varelas, T.
Trajectory Mining and Routing: A Cross-Sectoral Approach. *J. Mar. Sci. Eng.* **2024**, *12*, 157.
https://doi.org/10.3390/jmse12010157

**AMA Style**

Kaklis D, Kontopoulos I, Varlamis I, Emiris IZ, Varelas T.
Trajectory Mining and Routing: A Cross-Sectoral Approach. *Journal of Marine Science and Engineering*. 2024; 12(1):157.
https://doi.org/10.3390/jmse12010157

**Chicago/Turabian Style**

Kaklis, Dimitrios, Ioannis Kontopoulos, Iraklis Varlamis, Ioannis Z. Emiris, and Takis Varelas.
2024. "Trajectory Mining and Routing: A Cross-Sectoral Approach" *Journal of Marine Science and Engineering* 12, no. 1: 157.
https://doi.org/10.3390/jmse12010157