An Ensemble Imbalanced Classification Framework via Dual-Perspective Overlapping Analysis with Multi-Resolution Metrics

Abstract

The coexistence of class imbalance and overlap poses a major challenge in classification and significantly limits model accuracy. Data-level methods alleviate class imbalance by generating samples, but without ensuring their rationality, which may introduce noise. Algorithm-level methods are designed based on the model training process, avoiding noise introduction. However, existing methods often fail to consider the potential multiclass scenarios within overlap regions or design targeted solutions for different overlap patterns. This paper proposes an ensemble imbalanced classification framework via dual-perspective overlapping analysis with multi-resolution metrics. The dataset is divided into multiple resolutions for independent analysis, capturing distributional information from local to global levels. For each independent resolution, overlap is analyzed from the perspectives of “feature overlap” and “instance overlap” to derive more refined overlap scores. Flow model mapping and importance weighting are, respectively, applied to refine overlapping samples according to the two criteria. During testing, classifiers are adaptively selected based on the overlap degree of test samples under different criteria, and predictions across resolutions are integrated for the final decision. Experiments on 39 datasets demonstrate that the proposed method outperforms typical imbalanced classification methods in F-measure and G-mean, with particularly notable gains on 15 severely overlapping datasets.

1. Introduction

Classification problems hold a significant position in machine learning, with binary classification as the foundation. Due to data collection biases and natural class rarity, real-world datasets often exhibit long-tailed distributions [1], where minority class samples are critical for decision-making (e.g., disease detection [2], anomaly detection [3] and fraud identification [4]). Recent studies reveal that class imbalance is not the sole factor affecting classification performance. Sample overlap between different classes also significantly impacts model learning ability. Consequently, reasonable partitioning and targeted handling of overlapping regions have become a critical research topic.

In previous research, methods addressing class imbalance have primarily been categorized into two types: algorithmic-level approaches [5,6,7,8] and data-level approaches [9,10,11,12,13,14]. Algorithmic-level methods focus on mitigating feature bias that occurs during the model’s learning process. By artificially adjusting the model structure or designing loss weights, these methods ensure that the model pays more attention to the classification accuracy of minority class samples during training. Data-level methods, on the other hand, address the imbalance in the number of samples directly. Techniques such as oversampling or generative models are employed to augment the number of minority class samples, thereby balancing the numerical disparity between classes and preventing the model from developing biases due to learning from imbalanced datasets. Additionally, some researchers have considered the adverse effects of data overlap on model learning. They often define the degree of overlap autonomously and design rules for region partitioning, which, to some extent, assists the model in distinguishing samples within overlapping regions.

Existing methods address imbalance through data-level approaches (sampling, generation) [9,10,11,12,13,14] or algorithm-level approaches (cost-sensitive learning, ensemble methods) [5,6,7,8]. However, they suffer from two critical limitations: (1) Single-perspective overlap analysis: Current methods primarily rely on instance-level neighborhood analysis (e.g., k-Nearest Neighbors), failing to capture feature-space overlap patterns; (2) Fixed-scale measurement: Using a single neighborhood range cannot comprehensively characterize multi-modal overlap distributions across local and global scopes.

Data-level methods address the issue of class imbalance directly through sampling and generation techniques, thereby mitigating the decision bias problem during model training. Algorithm-level methods, on the other hand, achieve additional focus on minority class samples by means such as adaptive weight adjustment, avoiding overfitting issues caused by numerical imbalance. However, these methods not only suffer from inherent limitations but also lack an effective mechanism for identifying and handling overlapping regions within datasets. The insufficient consideration of overlap issues restricts the classification performance of these methods, preventing them from fully leveraging their algorithmic potential. Therefore, how to conduct a fine-grained analysis of the overlap degree across the entire dataset and design targeted solutions based on overlap metrics is a pressing problem that needs to be addressed. This paper proposes an ensemble imbalanced classification framework via dual-perspective overlapping analysis with multi-resolution metrics (DPOA-MRM). It utilizes “feature overlap” and “instance overlap” as two complementary pieces of information synergistically within the same framework for the first time, and achieves hierarchical overlap measurement from local to global levels through a multi-resolution strategy. This framework not only breaks through the limitations of traditional methods that rely on a single neighborhood range but also avoids information loss caused by resolution selection bias, thereby providing a more reliable foundation for the subsequent refined processing of overlapping samples. Specifically, the “multi-resolution” strategy effectively balances local details and global structure by independently calculating sample overlap degrees under different spatial scales; the “dual-perspective” criteria delve into the complex relationships between classes from the dimensions of feature separability and neighborhood heterogeneity. The integration of the two not only improves the accuracy of identifying overlapping regions but also provides more targeted guidance for the subsequent selection and fusion of classifiers. Building on this, the method further refines the processing of overlapping samples by designing flow model mapping and importance weight calculation techniques tailored to the differences in overlap information obtained from the two perspectives. For each test sample, we calculate its overlap degrees under both perspectives across all resolutions. Classifiers matching the sample’s overlap profile are selected, and their confidence scores are integrated for final prediction. The main contributions of this paper are as follows:

•

A dual-perspective multi-resolution overlap measurement framework is proposed. We propose a unified framework that analyzes overlap from both “feature” and “instance” perspectives across multiple resolutions. This approach captures distributional information from local to global levels, overcoming the limitations of single-metric methods in identifying complex overlap patterns.

•

A method for overlapping feature separation based on flow model mapping is proposed. To address the “feature overlap” challenge, we design a flow model-based mapping strategy. This mechanism projects highly entangled samples into a lower-dimensional, separable latent space, significantly reducing the difficulty of learning discriminative features in boundary regions.

•

A method for calculating attention weights based on multi-nearest-neighbor distribution discrimination in the data neighborhood is proposed. Focusing on “instance overlap,” we develop an adaptive weighting scheme that categorizes samples based on their neighborhood heterogeneity. This enables the model to selectively prioritize hard-to-classify boundary samples while suppressing noise and redundant information from the majority class.

The structure of the subsequent sections of this paper is outlined below. Section 2 provides an overview of the prior research pertinent to this study. Section 3 details the proposed DPOA-MRM methodology. Subsequently, Section 4 outlines the experimental approaches and metrics for performance evaluation that were employed to substantiate our methodology. Finally, Section 5 concludes the paper.

2. Related Work

This paper addresses the shortcomings of existing methods for imbalanced classification and proposes an integrated imbalanced classification method based on multi-resolution overlap measurement and dual-perspective overlap criteria. The related prior work associated with this paper can be mainly divided into three parts: (1) Data-level imbalanced classification methods; (2) Algorithm-level imbalanced classification methods; (3) Relevant work on overlap region division.

2.1. Data-Level Imbalanced Classification Methods

Data-level balancing approaches address class imbalance through dual strategies: either expanding the representation of the minority class or reducing the number of instances in the majority class. Current methodologies predominantly bifurcate into resampling techniques and generation-driven solutions. Resampling mechanisms operate through dataset distribution analysis, either creating synthetic instances (oversampling) or eliminating redundant samples (undersampling). The SMOTE framework (Synthetic Minority Over-sampling Technique) [9] exemplifies this paradigm, employing KNN (k-Nearest Neighbors) [15]-guided random linear interpolations between minority instances to counteract overfitting risks inherent in naive oversampling. Subsequent enhancements to this foundation have emerged, including methodologies detailed in [16] that introduce localized density metrics for minority samples alongside hybrid cleansing protocols. These advanced techniques eliminate majority class intrusions in overlapping feature spaces while establishing weighted sampling criteria informed by decision boundary adjacency and regional density, facilitating synthetic generation across both core and marginal data regions. Nevertheless, such resampling strategies primarily address data distribution disparities without effectively harnessing intrinsic sample characteristics, resulting in synthetic outputs that fail to preserve original feature integrity and may inadvertently incorporate extraneous noise.

Contemporary investigations have concurrently addressed challenges related to boundary ambiguity through enhanced sampling methodologies. Conventional SMOTE implementations [9] inherently exhibit limitations in handling class overlap areas, occasionally exacerbating decision boundary complexity through synthetic instance generation. In response, the SMOTE-NaN-DE framework [17] introduces dual innovations: natural neighbor error analysis for noise/boundary detection and differential evolutionary optimization for refined sample placement. This synergistic mechanism enhances interclass separability while maintaining original data integrity, though its capacity to exploit nuanced overlap patterns remains underdeveloped. Parallel developments include MPP-SMOTE [18], which conducts a comparative analysis of interpolation paradigms, strategically blending linear and feature-space augmentation based on classification complexity metrics. This hybrid approach minimizes emergent overlap artifacts during synthesis by utilizing localized feature interpolation, which is particularly effective for boundary-proximate samples that exhibit high discriminative uncertainty. HSCF [19] accurately locates information-rich areas by dynamically dividing feature intervals and calculating density ratios and proposes a hybrid sampling framework that balances oversampling and undersampling adaptively, thereby avoiding overfitting and information loss and achieving a more balanced data distribution. Nevertheless, both methodologies demonstrate constrained effectiveness in resolving intrinsically ambiguous overlap patterns inherent in high-dimensional imbalanced contexts. Sampling methods fail to learn overlapping region features and rely solely on neighbor class distribution, limiting performance improvements.

Generation-based methods learn the features of minority class samples through deep models and generate new samples to achieve sample balance. The commonly used deep generative models are mainly Variational Autoencoders (VAEs) [13] and Generative Adversarial Networks (GANs) [14]. VAE is an improvement of the Autoencoder (AE), which introduces the Evidence Lower Bound (ELBO) from variational inference to address the issue of difficult-to-predict posterior distributions of generated samples in AE, allowing it to describe observations of the latent space probabilistically. GAN leverages the idea of adversarial training by constructing an additional discriminator that competes with the generator during training, thereby enhancing the realism of the generated samples.

Recent advancements have witnessed domain-specific enhancements of these foundational architectures. Notably, literature [20] synergized variational autoencoders with attention mechanisms for enhanced partial discharge diagnostics in geospatial monitoring systems. Concurrently, literature [21] has devised VLAD, a lifelong learning framework that merges VAE architectures with experience replay and structured memory consolidation for adaptive anomaly detection, while such task-oriented adaptations demonstrate improved performance, they lack generalized quality assurance for synthesized instances. Complementary innovations include WGAN-GP [22] extension incorporating conditional constraints to better approximate sample distributions, thereby enhancing the realism of synthetic outputs for imbalance mitigation. Pioneering work by literature [23] established GAN-based minority sample generation with dual quantitative metrics: MMD for distribution divergence analysis and silhouette coefficients for cluster separability evaluation, setting new benchmarks for synthetic sample assessment. These developments collectively highlight the field’s progression towards more sophisticated generation-evaluation pipelines, though fundamental challenges in sample validity preservation persist.

Deep architectures inherently demand substantial parametric complexity, posing challenges in imbalanced classification scenarios where dataset scales frequently prove inadequate for supporting such intricate models. Particularly in cases of extreme class disproportion or absolute scarcity of minority instances, the paucity of discriminative features severely restricts models’ capacity to synthesize statistically reliable samples for imbalance correction. Targeting this limitation, contemporary research emphasizes mining intricate feature patterns within overlapping instances through enhanced generative frameworks. The ADA-INCVAE [24] methodology, evolved from VAE foundations, implements neighborhood distribution analysis to quantify permissible generation scopes and volumes, thereby strategically constraining synthetic instance production to minimize overlap expansion. Parallel innovations include RGAN-EL [25], a GAN-derived architecture that amalgamates hybrid generator loss functions with selective filtration mechanisms to elevate sample fidelity. This approach further integrates ensemble learning principles to boost model generalizability. Complementarily, RVGAN-TL [26] introduces probabilistic overlap quantification through roulette-based minority sample selection, enabling focused extraction of information-dense patterns from boundary regions via transfer learning paradigms.

These methods have addressed existing issues in each model and proposed solutions for the overlapping region, achieving some degree of additional attention to the feature information of overlapping samples and obtaining certain results. Generation-based methods often choose to perform additional feature learning on overlapping samples to enable models to better synthesize information-rich overlapping samples during the generation of new samples, thereby enhancing the learning ability of subsequent classification models. The problems with this approach are as follows: First, the rationality of the generated new samples lacks a mechanism for assurance. Second, whether the generated overlapping samples are beneficial to the learning of subsequent classifiers cannot be measured. Finally, the deep models used in generation-based methods make it difficult to leverage their advantages under limited sample conditions, and the quality of generated samples is often poor.

2.2. Algorithm-Level Imbalanced Classification Methods

Algorithm-level methods modify the loss functions or weight matrices of existing models. This enables models to focus more on minority class features during training. Cost-sensitive learning [27,28] is a representative approach in this category. Researchers have proposed various characteristic methods for addressing imbalanced classification through mathematical analysis and other means. The authors of [27] considered the differences in modeling errors among samples of different classes and assigned weights to samples based on their modeling errors. By minimizing the mean and variance of modeling errors, the study achieved the classification of imbalanced data. The authors of [28] proposed an adaptive-weight-based cost-sensitive support vector machine (SVM) ensemble method, using cost-sensitive SVM as the base classifier and integrating the results of base classifiers with an improved cost-sensitive Boosting scheme. This approach helps to bias the final decision boundary towards the minority class. However, cost-sensitive learning lacks broad applicability and often requires specific designs for particular problems to achieve satisfactory results. Moreover, the misclassification costs for specific problems are often difficult to obtain, and designing algorithms based solely on past experience is unlikely to yield optimal results, requiring extensive experimentation for validation. Additionally, focusing on minority class samples can easily lead to overfitting.

In addition to cost-sensitive learning, one-class learning and ensemble learning also hold important positions in algorithm-level methods. Typical one-class algorithms include SVDD [6] and iForest [7], which only require learning the features of a single class of samples. Therefore, the decision bias caused by the imbalance in the number of samples does not affect their performance, making them suitable for solving imbalanced classification problems. However, one-class learning ignores the feature information of minority class samples, resulting in suboptimal performance under mild imbalance conditions and limited generalizability. Ensemble learning methods are mainly divided into two categories: Bagging-based methods and Boosting-based methods, which are often combined with data-level sampling methods to obtain more diverse training datasets and more robust integrated results. Common base models such as RF [29], GDBT [30], and XGBoost [31] fall within the scope of ensemble learning. The authors of [32] proposed a hybrid sampling strategy that adaptively samples from the majority class and adds these samples to the minority class dataset. By dynamically adjusting the sampling weights, multiple training sets are generated, and the results of the base classifiers are integrated to obtain the final result. The authors of [33] first divided the dataset into different regions and then used different kernel functions to map boundary samples to higher dimensions. By integrating the results of multiple support vector machines, the study achieved a multiclass classification of imbalanced data. MDSampler [34] proposes an ensemble sampler based on meta-distribution, which integrates semi-supervised learning, imbalanced learning, and ensemble learning through iterative instance undersampling and cascade classifier aggregation. It not only improves the diversity of the model but also further improves the overall performance by integrating the advantages of multiple classifiers. However, although these methods provide more accurate and robust classification results, they are essentially simple combinations of weak classifiers, and their performance is limited by the inherent performance of the classifiers themselves. They fail to explore the feature differences between different classes of samples thoroughly.

Contemporary algorithmic innovations have emerged to tackle interclass data overlap challenges through multiple strategic dimensions. RUE [35] established spatial localization metrics coupled with cost distribution mechanisms, evaluating sample significance through distributional patterns and positional correlations to determine misclassification penalties. PCGDST-IE [36] introduced a combined clustering and dimensional compression approach, restructuring training data into simplified distribution subgroups. Subsequent overlap resolution and rebalancing processes within each subgroup amplified minority class prominence in overlapping zones while optimizing subgroup differentiation. HDAWCR [37] and AWLICSR [38] employed spatial density analyses across intraclass and interclass relationships, utilizing spatial theory principles to augment the classification efficacy of the Collaborative Representation-based Classification (CRC) [39] paradigm. DPHS-MDS [40] implemented zonal partitioning through majority class neighborhood density analysis, segmenting feature space into four distinct regions. This framework adaptively applies region-specific hybrid sampling techniques and deploys tripartite ensemble architectures, dynamically activating optimal classifiers based on the spatial configurations of test instances.

Algorithm-level methods, which are based on expert experience and mathematical derivation, have been designed to address specific tasks by modifying the loss functions or weights. These modifications can, to some extent, alleviate the decision bias caused by data imbalance. However, these methods do not fundamentally solve the problem of data imbalance. Moreover, the approach of modifying weights does not facilitate the model’s ability to extract feature information from the samples more effectively. As a result, algorithm-level methods are often limited by the specific tasks and datasets to which they are applied, lacking generalizability. Additionally, when dealing with datasets that have complex and diverse overlapping situations, a single algorithm may struggle to cover all overlapping scenarios, thus limiting the upper bound of its performance.

2.3. Relevant Work on Overlap Region Division

In imbalanced classification, sample overlap is considered the primary issue affecting model accuracy. Its impact often exceeds that of data imbalance itself. Data overlap and data imbalance are not strongly correlated. They exist independently in various datasets as distinct manifestations of data distribution characteristics. However, for classification problems, the coexistence of data overlap and data imbalance significantly increases the difficulty for models to correctly learn the differences between classes and make accurate class judgments.Limited minority samples make overlapping features harder to learn. On the other hand, the imbalance within the overlapping region further complicates the already complex and difficult-to-handle overlap area, making it harder to locate and address specifically. Overlap handling has become critical in imbalanced classification, with studies in information fusion, finance [41], healthcare [42], software [43], and network systems [44].

Considering that the manifestation of data overlap exists not only at the data distribution level but also at the feature level, researchers have conducted in-depth studies and explorations on the localization and division of overlapping regions, proposing a variety of methods for identifying overlapping areas. Currently, the main methods for dividing overlapping regions can be categorized as follows:

1. Feature Overlap: Feature overlap focuses on regions with low class separability. Researchers use projection and distribution-based identification methods. Literature [45] estimated the descriptors of data space distribution and the shape and size of decision boundaries to measure classification complexity, thereby identifying feature overlap regions in the dataset. The classification complexity can be used to estimate the difficulty of separating data points into their respective classes, thus locating regions with low class separability. However, the measurements derived from feature overlap are based on the assumption of continuous features. Moreover, measurements based on feature space division are susceptible to the concept of separation and noisy data, which limits their applicability.

2. Instance Overlap: Instance overlap measures local characteristics through neighborhood analysis rather than global features. The most common measurement method combines this “complexity” with the k-Nearest Neighbors (kNN) classifier, which measures the overlap degree by analyzing the number of heterogeneous samples within the neighborhood of the current sample. The authors of [46] improved existing model-based measurement standards by incorporating data imbalance rate indicators during the estimation process, proposing an Augmented R-value metric. The study also provided theoretical proof and empirical validation of the effectiveness of the new measurement standard in estimating overlap. However, instance overlap often focuses only on the nearest neighbors surrounding a sample, extracting overlap information from local information and lacking a global perspective. When the dataset contains multiple overlapping regions or multiple distribution patterns, instance overlap often struggles to identify complex overlapping ranges accurately.

3. Structural Overlap: Structural overlap measurement, which is related to the complexity of data morphology, is considered a good indicator for identifying class overlap. As previously analyzed, class overlap accumulates a large number of complexity sources, including both feature space overlap and neighborhood overlap. In addition, the topology, shape, or structure of the data itself may have hidden dependencies on the degree of overlap. On the one hand, the global characteristics of the domain affect the identification of problematic regions, thereby influencing the quantification and representation of class overlap. On the other hand, class overlap directly affects the shape of decision boundaries between classes and may introduce additional complexities, such as class skewness, which alters the structural properties of the domain. The authors of [47], from the perspective of meta-learning, analyzed the relationship between the performance of existing methods and various data complexity metrics, using only metrics calculated from the data to determine the best-performing method for a given dataset. This study provided targeted improvements to existing metrics.

Existing methods identify overlaps independently without integration, limiting their ability to precisely localize overlapping regions. From the analysis of existing work in the field of imbalanced classification, it is evident that the current methods for dividing overlapping regions often rely solely on instance-based division, which means that only local information within the sample neighborhood can be captured. Existing methods neither consider the differences in overlap degrees of the same samples from different perspectives nor conduct refined processing of overlapping samples obtained under different overlap measurement conditions. How to comprehensively assess the degree of overlap from a multi-resolution perspective, ranging from global to local, and design corresponding overlap sample processing methods that match the characteristics of different overlap measurements is a key challenge in solving imbalanced classification problems.

3. The Proposed Method: DPOA-MRM

Algorithm-level methods address classification boundary shift by designing loss functions or modifying weight matrices, while achieving relatively accurate results, these methods lack generalizability. Data-level methods synthesize new samples by learning features and spatial distributions. Sampling methods, however, do not learn inherent data features. Generation-based methods cannot verify sample rationality, potentially introducing noise. Generation-based methods, although learning sample features through deep networks, cannot verify the rationality and effectiveness of the generated samples, potentially introducing additional noise. Existing methods use only local neighborhood information and single-scale measurement, causing inaccurate overlap localization. The proposed framework integrates multi-resolution analysis (global to local) with dual-perspective criteria (feature and instance) to accurately identify overlapping regions. This addresses neighborhood range selection challenges while capturing comprehensive overlap information. On this basis, for each independent resolution scenario, the degree of data overlap is calculated from both the “feature overlap” and “instance overlap” perspectives. The dual-perspective overlap calculation method facilitates an in-depth exploration of the complex feature relationships between samples of different classes and the distribution information within the neighborhood space, thereby yielding more refined and accurate overlap scores and avoiding the one-sidedness of single-perspective information. To further analyze and process the identified overlapping regions, the method employs flow model mapping and importance weight calculation techniques to refine the handling of two types of overlapping samples: those identified by feature overlap and those identified by instance overlap. During the testing phase, the feature overlap and instance overlap degrees of each test sample are first calculated. Based on these, a set of classifiers matching its overlap state is selected, and the final precise and robust classification result is obtained by integrating the class confidence scores from these classifiers.

3.1. The Framework for Overlap Degree Analysis Based on Dual-Perspective and Multi-Resolution Measurements

Current methods face two critical limitations: (1) fixed neighborhood ranges fail to capture multi-scale overlap patterns; (2) single-perspective analysis (instance-only or feature-only) cannot comprehensively characterize complex overlaps. Our multi-resolution dual-perspective framework directly addresses these limitations. This is essential for subsequent targeted processing of overlapping samples. Additionally, instance-based overlap analysis focuses on the distribution of samples within the neighborhood, primarily considering the internal spatial distribution patterns of the dataset. However, overlap situations in various datasets are complex and diverse, and analyzing overlap from a single perspective is insufficient for obtaining detailed and accurate results. To address these issues, a framework for overlap degree analysis based on dual-perspective and multi-resolution measurements is proposed. This framework aims to provide a more comprehensive understanding of overlap by integrating different perspectives and resolutions. The entire process of DPOA-MRM is shown in Figure 1.

Firstly, for the dataset to be processed, the degree of overlap is analyzed from the dual perspectives: “feature overlap” and “instance overlap.” The feature overlap analysis consists of two parts: feature selection and overlap degree calculation. Initially, the complexity and importance of the original features are analyzed using the F1 (Maximum Fisher’s discriminant ratio) metric and the Random Forest (RF) algorithm. Based on this, important and less complex features are selected to form a new feature space, and the distribution of the current feature space is analyzed to obtain the overlap degree for each sample. The instance overlap analysis is based on the k-Nearest Neighbors (kNN) algorithm to explore the neighborhood range of samples. Different overlap categories are divided according to the data distribution characteristics and the importance of different class samples, thereby achieving a refined instance overlap analysis. Multi-resolution measurement addresses single-range limitations by analyzing overlap at five scales. At each resolution:

Feature overlap: Flow model mapping reduces feature complexity.

Instance overlap: Overlap scores augment training data as attention weights.

This dual processing strategy matches the distinct characteristics of each overlap type.

Based on the predefined multi-resolution parameters, multiple sets of feature and instance overlap analysis results and multiple classifiers are obtained under different analysis ranges. By placing the test samples into the original feature space for overlap degree analysis and calculating the corresponding classification results, the final prediction class is obtained by integrating multiple sets of classification results.

Adopting a multi-resolution strategy is crucial because overlap phenomena are scale-dependent. A fixed neighborhood size may miss global structural overlaps or overfit to local noise. By analyzing data across varying resolutions, our framework captures both fine-grained boundary details and broader distributional trends. Resolution-adaptive weighting (Equation (1)) automatically balances the two perspectives. With a small neighborhood (S), the instance-based metric is susceptible to local noise. In contrast, feature-based metrics (calculated globally or on subsets) provide more stable guidance at this fine granularity. Therefore, as S increases, reliance is shifted towards the instance distribution.

$$\delta =\left\{\begin{array}{c}1-{\displaystyle \frac{\sqrt{S}}{m}}\\ {\displaystyle \frac{\sqrt{S}}{m}}\end{array}\right.,$$

(1)

where m is a hyperparameter used to control the magnitude of the weight $\delta$; S represents the number of neighboring samples examined in the feature space at the current resolution, which reflects the spatial scope considered when analyzing the degree of overlap to some extent.

This integrated approach compensates for single-scale, single-perspective limitations, effectively addressing multi-modal overlap phenomena for targeted processing.

3.2. Hybrid Feature Separation Method Based on Flow Model Mapping

Most methods classify samples in the original feature space. Classifier performance is often limited by complex decision boundaries and severe interclass overlap. Mapping samples to a latent space with simpler distributions can effectively alleviate these issues. This reduces classification difficulty. Following this rationale, for the mixed features identified through feature overlap calculation, a flow model is introduced to map them into a low-dimensional, highly separable space. These mapped features are then fed into the classifier for feature learning, effectively mitigating the challenge of learning overlapping features in the original space, as illustrated in Figure 2 below.

Flow models employ reversible transformations to map overlapping samples into low-dimensional spaces. This preserves discriminative information while reducing feature complexity. The three-component architecture (Figure 3), comprising a normalization layer, a reversible transformation layer, and an affine coupling layer, enables effective nonlinear feature disentanglement for improved separability.

In the model, the input sample is denoted as $X=\left\{{\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_m\right\}$, and the inputs and outputs of each module are represented as u and v, respectively. The flow model consists of three components:

(1) Sample Normalization Layer:

Stabilizes training via learnable transformations (Equation (2)):

$$v=p\odot u+d,$$

(2)

where ⊙ denotes the element-wise multiplication of vectors. The loss for the sample normalization layer can be expressed as:

$$Loss=-\sum _{k=1}^{n}log\left|{\mathbf{s}}_k\right|,$$

(3)

where $s_k$ represents the $k-th$ element of the vector.

(2) Invertible Transformation Layer:

In the invertible transformation layer, the sample dimensions consist of two parts: the first part remains consistent with the original dimensions, while the other part undergoes an affine transformation. To preserve the association information between original samples to the greatest extent during the transformation, a certain degree of permutation transformation is applied to the sample feature dimensions before the sample enters the affine coupling layer. To ensure the invertibility of the mapping, a 1 × 1 invertible transformation is introduced to replace the random shuffling operation in traditional flow models. The sample after the invertible transformation can be represented as:

$$v=Hu,$$

(4)

where H represents a randomly initialized

$$n\times n$$

matrix. The loss function for the invertible transformation layer can be expressed as:

$${Loss}_P=-log\left|det\left(H\right)\right|.$$

(5)

(3) Affine Coupling Layer:

The affine coupling layer was first proposed in [48], which addressed the issue of the difficult computation of the Jacobian determinant in the original flow model and further maintained the invertibility of the model. The affine coupling layer divides the original sample into two parts, $u_{1:d}$ and $u_{d+1:n}$, where $1:d$ denotes the first to the $d-th$ dimensions of the sample, and $d+1:n$ denotes the $(d+1)-th$ to the $n-th$ dimensions of the sample. The affine coupling layer applies an affine transformation to $u_{d+1:n}$, while $u_{1:d}$ remains unchanged. The scale transformation p and the shift transformation d of the affine transformation are obtained by the nonlinear transformation $NN$, and can be specifically expressed as:

$$p,d=NN\left(u_{1:d}\right),$$

(6)

The features $u_{d+1:n}$ after the affine transformation can be expressed as:

$$v_{d+1:n}=p\odot u_{d+1:n}+d,$$

(7)

Therefore, the Jacobian matrix of the invertible transformation can be expressed as:

$${\displaystyle \frac{\partial z}{\partial x}}=\left[\begin{array}{cc}{I}_d& 0\\ {\displaystyle \frac{\partial v_{d+1:D}}{\partial u_{1:d}}}& {\displaystyle \frac{\partial v_{d+1:D}}{\partial u_{d+1:D}}}\end{array}\right]=\left[\begin{array}{cc}{I}_d& 0\\ {\displaystyle \frac{\partial v_{d+1:D}}{\partial u_{1:d}}}& diag\left(s\right)\end{array}\right],$$

(8)

where $I_d$ denotes the d × d identity matrix, and $diag\left(s\right)$ represents the diagonal matrix with s as its diagonal elements. The loss for the affine coupling layer can be expressed as:

$${Loss}_A=-\sum _{k=1}^{n-d}log\left|s_k\right|.$$

(9)

Directly classifying samples in the original feature space is often suboptimal due to the intricate entanglement of minority and majority class features. The flow model is essential here as it creates a nonlinear mapping to a latent space where class boundaries become more distinct, thereby simplifying the subsequent classification task.

(1) Specific Structure of the Flow Model

The adopted flow model is mainly composed of three reversible transformation layers stacked sequentially. Its core idea is to transform the complex original feature distribution into a tractable base distribution (such as a standard normal distribution) through a series of bijective mappings. The overall architecture is shown in Figure 3. The model input is the selected feature-overlapping sample set X. This model is a sequence composed of L flow steps. Each flow step contains the following three sub-layers:

Activation Normalization Layer: As the first sub-layer, it applies an affine transformation to the data of each dimension for initial normalization. Its parameters (scale s and bias b) are calculated based on the mean and variance of the first batch of training data during initialization and are updated during training.

Invertible 1 × 1 Convolution Layer: As the second sub-layer, it replaces the traditional random permutation operation. It performs an intelligent shuffle of feature dimensions through a learnable rotation matrix W (initialized as an identity matrix) to enhance the model’s expressive power.

Affine Coupling Layer: As the core sub-layer, it splits the input u into $u_1$ and $u_2$. $u_1$ remains unchanged and is input into a sub-neural network, which outputs the scale factor (s) and translation amount (t) used to transform $u_2$. The transformation formula is: $v_2=u_2\odot exp\left(s\left(u_1\right)\right)+t\left(u_1\right)$, while $v_1=u_1$. Finally, $v_1$ and $v_2$ are concatenated as the output.

The sub-neural network in the coupling layer is a simple Multi-Layer Perceptron (MLP), with the structure including: (i) Input layer: dimension d (when the dimension of u is n, $d=n/2$); (ii) Hidden layers: 2 layers, with $4d$ neurons per layer; (iii) Activation function: LeakyReLU (negative slope = 0.01) for hidden layers; (iv) Output layer: dimension $n-d$, the output vector is split equally into scale factor s and translation amount t.

(2) Detailed Description of the Training Process

The training objective of the flow model is to maximize the probability of the mapped data in the log-likelihood space. According to the change of variable formula, the loss function is defined as the Negative Log-Likelihood (NLL):

$$L=-E\left[log{p}_Z\left(f\left(x\right)\right)+log\left|det\left({\displaystyle \frac{\partial f}{\partial x}}\right)\right|\right]$$

(10)

where f is the entire flow transformation, $p_Z$ is the prior distribution (standard normal distribution), and the second term is the logarithm of the determinant of the Jacobian matrix of the transformation, used to measure volume change.

Regarding training settings, the feature-overlapping sample set was randomly split into a training set and validation set at a 4:1 ratio; use the Adam optimizer; set the initial learning rate to $1\times {10}^{-3}$; dynamically adjust the batch size based on the dataset size, set to min(256, N/10), where N is the number of training samples; employ an early stopping strategy for training epochs, stopping when the loss on the validation set does not decrease for 20 consecutive epochs, with the maximum epochs set to 1000.

(3) Explanation of Key Parameter Settings

Flow Steps (L): Selection was made from 4, 6, 8, 10 via grid search and it was determined that $L=8$ achieves the best results on most datasets, striking a balance between complexity and expressive power.

Latent Space Dimension: The input and output dimensions of the flow model remain consistent with the original feature dimensions. The goal is feature disentanglement rather than dimensionality reduction. The mapped features retain the integrity of the original information, but the distribution is easier for the classifier to learn.

Sub-network Hidden Layer Size: Set to $4d$. This is an empirical value intended to provide sufficient nonlinear transformation capability while avoiding overfitting.

The training process of the flow model is shown in Algorithm 1.

Theoretical advantages of the flow model and the argumentation for improving interclass separability are as follows:

(1) Theoretical Value of Reversibility:

The flow model is based on the essence of reversible transformation, ensuring information losslessness and precise probability density transformation.

Information Losslessness: The invertible mapping $f:R^d\to R^d$ ensures that all discriminative information of the original feature space can be retained in the low-dimensional space. Mathematically, reversibility ensures $f^{-1}\left(f\left(x\right)\right)=x$, meaning the low-dimensional representation $z=f\left(x\right)$ preserves all feature information of the original sample x. In class overlap regions, discriminative features between samples of different classes are often very subtle, possibly reflected only in minute differences in certain feature dimensions. Traditional dimensionality reduction methods (like PCA retaining principal components) might lose this crucial but low-variance discriminative information, causing originally separable samples to become inseparable after reduction. The information losslessness of the flow model ensures that even the subtlest discriminative features can be preserved in the low-dimensional space, allowing the classifier to accurately distinguish overlapping samples in the simplified feature space.

Algorithm 1 The calculation process of feature overlap.

Require: Training dataset ${\mathbf{D}}_{train}=\left\{({\mathbf{x}}_i,y_i)\right|i\in N\}$, the training epochs of flow model $epoch$, The number of samples sampled during each training of the flow model $batchsize$.

Ensure: Feature overlapping sample set ${\mathbf{D}}_{overlap}$; Non overlapping feature sample set ${\mathbf{D}}_{non-overlap}$; Trained Flow Model ${\theta }_{flow}$; Trained feature overlapping sample classifier ${\theta }_{overlap-cls}$; Trained feature non overlapping sample classifier ${\theta }_{non-overlap-cls}$;

1: for $f_i$ in $[f_1, f_2, ..., f_n]$ do   2:      $F_i={\displaystyle \frac{{({\mu }_{f_{i0}}-{\mu }_{f_{i1}})}^2}{{\sigma }_{f_{i0}}^2-{\sigma }_{f_{i1}}^2}}$   3: end for   4: Obtain the degree of overlap of all features $F=[F_0, F_1, ..., F_n]$   5: Use random forest to calculate the importance of all features $I=[I_0, I_1, ..., I_n]$   6: Obtain a comprehensive discrimination index for feature importance based on the degree of feature overlap and importance $P=F\odot I=[F_0·I_0, F_1·I_1, ..., F_n·I_n]=[P_0, P_1, ..., P_n]$   7: Obtain the maximum feature importance level $P_{sub}=[P_i, P_j, ..., P_t]$ that occupies the top of the total and its corresponding feature $F_{sub}=[f_i, f_j, ..., f_t]$   8: for $f_i$ in $F_{sub}$ do   9:      $\mathbf{subD}=[{\mathbf{D}}_{train}[:, f_i], \mathbf{y}]$ 10: end for 11: Obtain the feature overlap degree of each sample by integrating the importance of features and the instance overlap degree of subsets $Fea=[In{s}_{\mathbf{subD}-i}^T,In{s}_{\mathbf{subD}-j}^T,...,In{s}_{\mathbf{subD}-t}^T]\ast P_{sub}$ 12: $\phi ={\displaystyle \frac{Foc}{\sqrt{S-N_{diff}}+1}}\ast Ig$ 13: Divide the training set into feature overlapping sample set ${\mathbf{D}}_{overlap}$ and feature non overlapping sample set ${\mathbf{D}}_{non-overlap}$ based on the feature overlap degree 14: Initialize flow model ${\theta }_{flow}$ and feature overlapping sample classifier ${\theta }_{overlap-cls}$ 15: ${\theta }_{flow}\leftarrow {\nabla }_{{\theta }_{flow}}\left({\theta }_{flow}\left({\mathbf{D}}_{overlap}\right)\right)$, ${\theta }_{overlap-cls}=RF\left({\mathbf{D}}_{overlap}\right)$ 16: ${\theta }_{non-overlap-cls}=RF\left({\mathbf{D}}_{non-overlap}\right)$ 17: return ${\mathbf{D}}_{overlap}$, ${\mathbf{D}}_{non-overlap}$, ${\theta }_{flow}$, ${\theta }_{overlap-cls}$, ${\theta }_{non-overlap-cls}$

Precise Density Transformation: Through the precise calculation of the Jacobian determinant (Equation (8)), the probability density of the transformed space is $p_Z\left(z\right)=$$p_X\left(x\right){\left|det(\partial f/\partial x)\right|}^{-1}$. This allows the model to accurately model sample distribution in the low-dimensional space, rather than relying on approximate inference like VAE. Precise probability density modeling is crucial for the classification of overlapping samples. In overlapping regions, probability distributions of different classes intertwine, and classification decisions inherently rely on the accurate estimation of the posterior probability $\mathrm{p}\left(\mathrm{y}\left|x\right.\right)$. VAE uses the Evidence Lower Bound (ELBO) for approximate inference; this approximation introduces large errors in highly overlapping regions, leading to blurred class boundaries. In contrast, the flow model, through precise density transformation, can accurately calculate the class-conditional probability density of each sample point in the transformed space, enabling the Bayesian classifier to make more precise decisions.

(2) Mechanism for Overlapping Sample Separation:

How the flow model achieves separation of overlapping samples was explained in detail:

Nonlinear Feature Decoupling: The affine coupling layer (Equations (6) and (7)) decouples the entangled feature dimensions in the original space by learning the nonlinear transformation $\mathrm{NN}(·)$. Specifically, for samples in overlapping regions where interclass features are highly correlated, the flow model can learn a transformation such that the interclass differences of the transformed features in the new space are amplified, while intraclass similarities are maintained.

Adaptive Dimension Compression: Unlike linear dimensionality reduction with fixed projection directions, the flow model’s invertible transformation layer (Equation (4)) adaptively finds the optimal feature reorganization direction by learning the matrix H. This adaptivity is particularly important for overlapping samples because overlap often occurs in specific feature subspaces, and the flow model can map these problematic dimensions to a more separable space.

Hierarchical Feature Learning: The multi-layer flow model (Figure 3) achieves feature separation from coarse to fine granularity through layer-by-layer transformation. The first layer may separate major class features, while subsequent layers focus on subtle differences in boundary regions. This hierarchical mechanism is particularly suitable for handling complex situations with multi-modal overlap.

(3) Theoretical Demonstration of Improved Interclass Separability:

According to Bayes’ error rate theory, the lower bound of classification error depends on the degree of overlap of class-conditional probability densities:

$${\mathrm{P}}_{\mathrm{error}}\ge \int min\left\{p\left(x\left|C_0\right.\right),p\left(x\left|C_1\right.\right)\right\}dx.$$

(11)

Through the reversible transformation f, the flow model, while keeping the total probability mass unchanged, is able to learn a transformation such that:

$$\int min\left\{p\left(z\left|C_0\right.\right),p\left(z\left|C_1\right.\right)\right\}dz<\int min\left\{p\left(x\left|C_0\right.\right),p\left(x\left|C_1\right.\right)\right\}dx.$$

(12)

This reduces the overlap of class-conditional distributions in the transformed space, thereby lowering the lower bound of the theoretical error rate.

Through the above multilevel and multi-angle supplements, we believe we have fully clarified the theoretical advantages and practical value of flow model mapping.

3.3. Attention Weight Calculation Method Based on Multi-Neighbor Distribution Discrimination

During the analysis of instance overlap, the degree of overlap for a given sample is calculated by examining the number of heterogeneous samples within its neighborhood. However, not all samples warrant additional weighting or attention, as the importance of samples varies depending on their distribution patterns. Therefore, to comprehensively and accurately determine the overlap scores for different samples, a novel attention weight calculation method based on multi-neighborhood distribution discrimination is proposed. First, samples are categorized into the following three types based on their distribution characteristics, which is illustrated in Figure 4.

1. Low-overlap samples ($N_{diff}\le 1$): Predominantly homogeneous neighborhoods indicate easy-to-learn patterns. Lower weights (Equation (13)) prevent redundant learning.

2. High-overlap samples ($S-N_{diff}\le 1$): Predominantly heterogeneous neighborhoods represent rare patterns. Moderate weights (Equation (14)) ensure adequate learning without overemphasis.

3. Boundary samples (otherwise): Mixed neighborhoods indicate critical boundary regions. Highest weights (Equation (15)) ensure comprehensive learning of discriminative features.

For each sample x with S nearest neighbors, the overlap weight $\phi$ is calculated based on heterogeneous neighbor count $N_{diff}$:

When $N_{diff}\le 1$: In this case, only a small portion of the samples in the examined neighborhood range belong to different classes. Based on the earlier analysis, this distribution pattern is relatively common in the original data space, and the model can easily learn from such samples. For these samples, the model should pay relatively less attention during training to avoid overfitting, which could diminish its ability to distinguish challenging samples in overlapping regions. The corresponding overlap weight $\phi$ is calculated as follows:

$$\phi ={\displaystyle \frac{Foc}{\sqrt{S-N_{diff}}+1}}\ast Ig,$$

(13)

where $Foc$ represents the base attention level, a predefined hyperparameter that denotes the model’s baseline attention value for each individual sample. $Ig$ represents the ignore coefficient, which is set for samples with easily learnable distribution patterns and indicates the degree to which the model ignores such samples. For these samples, because their features are easy to learn, a certain reduction in attention is applied on top of the base attention level to prevent the model from overemphasizing easily learnable features at the expense of critical features in overlapping regions. This results in the final overlap weight.

When $S-N_{diff}<=1$: In this case, only a small portion of the samples in the examined neighborhood range belong to the same class. This distribution pattern occurs infrequently and may contain potential sample distribution patterns. Therefore, an appropriate increase in attention is considered to ensure that the model can recognize such distribution patterns. The overlap weight is calculated as follows:

$$\phi =Foc\ast \left[{\displaystyle \frac{1}{\sqrt{N_{diff}}}}+1\right].$$

(14)

For samples that do not fall into the above two categories, it can be assumed that they exhibit varying degrees of overlap. These samples contain relatively important overlapping feature information for classification tasks. Due to the mixed nature of their features and the spatially close distribution of samples from different classes, it is challenging for the model to learn the characteristics of such samples fully. Therefore, a higher level of attention is required for these samples to ensure that the model adequately learns the information they contain. The overlap weight is calculated as follows:

$$\phi =Foc\ast \left[\sqrt{N_{diff}}+1\right].$$

(15)

The calculated overlap weight is incorporated as an additional attribute of the corresponding target sample and is jointly input into the model for learning.

Not all samples contribute equally to the decision boundary. This adaptive weighting is important to prevent the model from being overwhelmed by the sheer volume of easy-to-classify majority samples (redundancy), ensuring it focuses its capacity on the information-rich but scarce samples located in the critical overlap regions.

The overlap weights calculation process is shown in Algorithm 2.

Algorithm 2 The overlap weights calculation process.

Require: Original dataset X, the size of the nearest neighbor pool S, The overall expansion factor of the dataset $Foc$.

Ensure: Target-neighbor sample combination dataset A;

for each x in X do

2:     $Nei=KNN(x,X,S)$   /* Among them, $Nei$ represents all samples except x, and $KNN(x,X,S)$ represents the S neighbor samples of x except itself in X. */     $N_{diff}=Judge\left(Nei\right)$         /* Among them, $N_{diff}$ the number of different class neighbors of sample x, $Judge\left(Nei\right)$ represents check every neighbor in the neighbor space $Nei$ and count the different class samples. */   4:     $if:S-N_{diff}<=1$     $\phi =Foc\ast \left[{\displaystyle \frac{1}{\sqrt{N_{diff}}}}+1\right]$   6:     $elseif:N_{diff}<=1$     $\phi ={\displaystyle \frac{Foc}{\sqrt{S-N_{diff}}+1}}\ast Ig$   8:     $else:$     $\phi =Foc\ast \left[\sqrt{N_{diff}}+1\right]$ 10:     $x=(x,\phi )$     $Add(x,A)$ 12: end for return A

In summary, the method proposed in this paper has significant innovations in the following three aspects: (1) it proposes a dual overlap measurement mechanism fusing feature perspective and instance perspective for the first time, breaking through the information bottleneck of traditional single perspectives; (2) it introduces a multi-resolution analysis framework to achieve multilevel overlap information extraction from local neighborhoods to global distributions; (3) it designs a differentiated processing strategy for overlapping samples based on flow model mapping and importance weighting, enhancing the model’s discriminative ability for hard-to-classify regions.The overall flowchart of DPOA-MRM is shown in Figure 5.

3.4. Algorithm Complexity Analysis

This section derives the DPOA-MRM from two dimensions: time complexity and space complexity, and compares it with existing mainstream ensemble imbalanced classification methods (based on MDSampler, DPHS-MDS, AWLICSR, and BRAF). All symbol definitions are consistent with the main text: N is the number of training samples, d is the original feature dimension, K is the number of resolution layers (default $K=5$), $S_{max}$ is the maximum neighborhood radius (default $S_{max}=9$), $T_{flow}$ is the number of iterations of the flow model, $T_{base}$ is the number of iterations of the base learner, E is the number of base learners (ensemble size).

3.4.1. Time Complexity

(1) Multi-resolution Overlap Measurement Stage

Feature Perspective: Calculating the importance of F1 and RF requires traversing all samples and features, with a complexity of $O\left(Nd\right)$; for K resolutions, scanning feature subsets $S_k\in \left\{1,3,5,7,9\right\}$ time, the total complexity is $T_1 = O\left(K·N·d·S_{max}\right) = O\left(5Nd·9\right)$$= O\left(Nd\right)$.

Instance Perspective: KNN search is performed at K resolutions. After acceleration with KD-Tree, the average single search is $O\left(logN\right)$, and the total for N samples is $T_2 = O\left(K·N·logN\right) = O\left(NlogN\right)$. Dual Perspective Fusion: Linear weighting, which $O\left(N\right)$ can be ignored. In summary, the total time complexity of the overlap measurement stage is $T_{overlap}=T_1+T_2=O\left(Nd+NlogN\right)$.

(2) Overlap Sample Processing Stage

Flow Model Mapping: The network forward/backward propagation only applies to the subset of samples judged as “feature overlap”. Let its ratio be $\alpha$, and each round traverses $\alpha N$ samples, reducing the dimension to $d^{\prime }=⌈d/2⌉$, with a single round complexity of $O\left(\alpha N{d}^{\prime }\right)$, and after $T_{flow}$ rounds, $T_{flowmap} = O\left(\alpha N{d}^{\prime }{T}_{flow}\right)$.

Importance Weighting: KNN searches again, with the same complexity as $T_2$, and the index can be reused, so the additional overhead is $O\left(N\right)$.

The total time complexity of this stage is $T_{process} = O\left(\alpha N{d}^{\prime }{T}_{flow} + N\right)$.

(3) Ensemble Training Stage

Train two RFs (overlapping/non-overlapping subsets) for each resolution. The RF training complexity is $O\left(N_{sub}·d·log{N}_{sub}·T_{base}\right)$, and the subset sizes are approximately $\alpha N$ and $\left(1-\alpha \right)N$, respectively. The ensemble of trees is $T_{train}=K·2·E·O(\alpha Ndlog\left(\alpha N\right)$$+\left(1-\alpha \right)Ndlog\left(\left(1-\alpha \right)N\right))= O(KENdlogN)$.

In summary, the total time complexity of the DPOA-MRM training stage is $T_{tra\mathrm{in}}^{total}$$=O(Nd+NlogN+0.15Nd{T}_{f}low+KENdlogN)=O\left(KENdlogN\right)$ (because $K,E,T_{flow}$ are of constant order of magnitude).

(4) Testing Stage

For a single test sample, perform a dual-view overlap calculation and tree prediction once at K resolution, with a complexity of $T_{test}=O\left(K\left(d+logN+ElogN\right)\right)$$=O\left(d+ElogN\right).$

3.4.2. Space Complexity

Original Data Storage: $O\left(Nd\right)$.

Multi-resolution KNN Index: KD-Tree has K trees in total, each tree has $O\left(N\right)$, totaling $O\left(KN\right)$.

Flow Model Parameters: The network weight size is proportional to d, approximately $O\left(d\right)$.

Ensemble Model: There are E trees, the upper bound of the number of nodes per tree is $O\left(N_{sub}log{N}_{sub}\right)$, totaling $O\left(K·2·E·NlogN\right)=O\left(KENlogN\right)$.

In summary, the peak space complexity is $S_{total}=O\left(KENlogN+Nd\right)$.

3.4.3. Comparison of Complexity with Existing Ensemble Methods

In

Table 1. Asymptotic Complexity of Various Ensemble Learning Methods at the Same Ensemble Scale (Constant Terms Omitted).

Method	Training Time Complexity	Testing Time Complexity	Peak Space Complexity
DPOA-MRM (ours)	$O\left(KENdlogN\right)$	$O\left(d+ElogN\right)$	$O\left(KENlogN+Nd\right)$
GBDT	$O\left(ENdlogN\right)$	$O\left(ElogN\right)$	$O\left(EN\right)$
RF	$O\left(EN\sqrt{d}logN\right)$	$O\left(ElogN\right)$	$O\left(EN\right)$
BRAF	$O\left(dk+EN\sqrt{k}logN\right)$	$O\left(logd+ElogN\right)$	$O\left(EN\right)$
DPHS-MDS	$O\left(NdlogN\right)$	$O\left(ElogN\right)$	$O\left(EN\right)$
SWSEL	$O\left(REw\sqrt{d}logw\right)$	$O\left(\alpha Elogw\right)$	$O\left(\alpha Ew\right)$
MDSampler	$O\left(E\sqrt{N}logN·logd\right)$	$O\left(ElogN\right)$	$O\left(E\sqrt{N}\right)$

, $k,R,w,\alpha$ represents the hyperparameters mentioned in the corresponding methods. The BRAF method reduces the d dimensional features to k through projection; the SWSEL method uses a sliding window to resample the nearest w samples in each round, and after training the subforest, only the best-performing $⌈\alpha E⌉$ trees are retained. The training round R is triggered by concept drift detection. The average depth of a single tree is uniformly estimated using $O\left(logN\right)$.

It can be seen that DPOA-MRM has the same order of magnitude in complexity as most mainstream ensemble methods, with training time complexity at the $O\left(NlogN\right)$ level, testing time complexity at the $O\left(logN\right)$ level, and peak space complexity at the $O\left(NlogN\right)$ level, but the difference in complexity between it and other methods is small. The multi-resolution strategy introduces a multiplier K that is acceptable at the constant level ($K=5$), and each resolution can be parallelized, further reducing the actual wall-clock time.

4. Experiments

This section conducts comprehensive performance evaluations of our ensemble classification framework for imbalanced data, which employs multi-resolution overlap quantification and dual-aspect boundary analysis. The experimental architecture comprises five components: Section 4.1 delineates the benchmark datasets and performance indicators. Section 4.2 specifies critical hyperparameter configurations, including multi-resolution granularities and neighborhood radii for overlap computation. Section 4.3 performs comparative analyses between our method and existing algorithm-level/data-level approaches in addressing class imbalance challenges. Section 4.4 conducts focused case studies on datasets exhibiting significant interclass overlap to demonstrate methodological superiority. Section 4.5 applies Nemenyi post hoc testing to validate statistical significance across comparative methods. Section 4.6 explores the sensitivity of DPOA-MRM to adjustable hyperparameters and their optimal value ranges through parameter sensitivity experiments. Ablation experiments are performed in Section 4.7 to verify the effectiveness and necessity of each module of DPOA-MRM.The complete specifications of all benchmarked techniques are systematically organized in

Table 2. Compared methods information.

Level	Method	Basis	Publication and Year
Algorithm	iForest [7]	One-class learning	ICDM 2008
	SVDD [6]		Applied Energy 2013
	GDBT [30]	Ensemble learning	Annals of statistics 2001
	RF [29]		Journal of Chemical Information and Computer Sciences 2003
	BRAF [49]		IEEE Transactions on Neural Networks and Learning Systems 2018
	DPHS-MDS [40]		Expert Systems with Applications 2020
	SWSEL [50]		Engineering Applications of Artificial Intelligence 2023
	MDSampler [34]		Pattern Recognition 2025
	PCGDST-IE [36]	Cost-sensitive learning	Information Sciences 2023
	HDAWCR [37]		Applied Intelligence 2024
	AWLICSR [38]		Expert Systems with Applications 2024
Data	SMOTE [9]	Sampling	Journal of Artificial Intelligence Research 2002
	Borderline-SMOTE [51]		ICIC 2005
	G-SMOTE [52]		ICPR 2014
	SMOTE-NaN-DE [17]		Knowledge-Based Systems 2021
	MPP-SMOTE [18]		Information Sciences 2023
	TSSE-BIM [53]		Information Sciences 2024
	HSCF [19]		Information Sciences 2025
	CTGAN [54]	Generating	NIPS 2019
	CWGAN-GP [22]		Information Sciences 2020
	ADA-INCVAE [24]		Applied Intelligence 2022
	RVGAN-TL [26]		Information Sciences 2023
	CDC-Glow [55]		Information Sciences 2023
	ConvGeN [56]		Pattern Recognition 2024
	SSG [57]		Neural Networks 2024

. Furthermore, the source code for DPOA-MRM is publicly available at GitHub (https://github.com/bupt-lqw/DPOA-MRM) (accessed on 29 November 2025).

4.1. Datasets and Evaluation Metrics

To comprehensively evaluate the proposed method’s performance, we selected 39 benchmark datasets from the KEEL machine learning repository [58]. This selection aims to minimize result bias by ensuring diversity in dataset attributes and imbalance characteristics. During dataset selection, we ensured maximum variation in imbalance ratios. We also considered additional factors, including sample size, overlap degree, and feature dimensions. This approach guarantees a reasonable distribution of attributes across different ranges. To demonstrate the superiority of our algorithm in handling significantly overlapping datasets, we adopted the F1 metric (Maximum Fisher’s Discriminant Ratio) [59] as a data complexity indicator. This measure computes feature-wise discriminant ratios and selects the maximum value across all features to quantify dataset intricacy. Elevated F1 scores correspond to intensified feature-space overlaps, reflecting heightened interclass ambiguity. Datasets exceeding threshold $0.4$ in F1 values were designated as having critical overlap severity. Key characteristics of these selected datasets are systematically presented in

Table 3. Characteristics of the selected datasets in the experimental verification.

Dataset	Instances	Features	Minority Instances	Majority Instances	IR	Overlap Degree
ecoli-0vs1	220	8	77	143	1.86	0.0367
wisconsin	683	10	239	444	1.86	0.0405
pima	768	9	268	500	1.87	0.5625
vehicle_2	846	19	218	628	2.88	0.6811
vehicle_1	846	19	217	629	2.9	0.8221
vehicle_3	846	19	212	634	2.99	0.8284
vehicle_0	846	19	199	647	3.25	0.5682
ecoli_1	336	8	77	259	3.36	0.3566
newthyroid1	215	6	35	180	5.14	0.0819
newthyroid2	215	6	35	180	5.14	0.0727
ecoli2	336	8	52	284	5.46	0.3416
segment0	2308	20	329	1979	6.02	0.4925
yeast3	1484	9	163	1321	8.1	0.3092
ecoli3	336	8	35	301	8.6	0.4916
page-blocks0	5472	11	559	4913	8.79	0.0640
yeast-2_vs_4	514	9	51	463	9.08	0.2896
ecoli-0-6-7_vs_3-5	222	8	22	200	9.09	0.0527
yeast-0-2-5-6_vs_3-7-8-9	1004	9	99	905	9.14	0.3108
yeast-0-2-5-7-9_vs_3-6-8	1004	9	99	905	9.14	0.3058
glass-0-4_vs_5	92	10	9	83	9.22	0.2508
ecoli-0-1-4-7_vs_5-6	332	7	25	307	12.28	0.2341
glass4	214	10	13	201	15.46	0.2434
ecoli4	336	8	20	316	15.8	0.2631
page-blocks-1-3_vs_4	472	11	28	444	15.86	0.0731
abalone9-18	731	9	42	689	16.4	0.4568
MEU-Mobile KSD	1071	72	51	1020	20	0.2848
yeast-2_vs_8	482	9	20	462	23.1	0.0000
flare-F	1066	12	43	1023	23.79	0.4131
kr-vs-k-zero-one_vs_draw	2901	7	105	2796	26.63	0.2681
kr-vs-k-one_vs_fifteen	2244	7	78	2166	27.77	0.0000
winequality-red-4	1599	12	53	1546	29.17	0.6376
yeast-1-2-8-9_vs_7	947	9	30	917	30.57	0.6547
abalone-3_vs_11	502	9	15	487	32.47	0.4092
kr-vs-k-three_vs_eleven	2935	7	81	2854	35.23	0.5400
ecoli-0-1-3-7_vs_2-6	281	8	7	274	39.14	0.0499
abalone-17_vs_7-8-9-10	2338	9	58	2280	39.31	0.0747
yeast6	1484	9	35	1449	41.4	0.3550
poker-8-9vs6	1485	11	25	1460	58.4	0.9367
poker-8vs6	1477	11	17	1460	85.88	0.9297

.

In the field of imbalanced classification, minority class samples are often of greater concern. However, while maintaining model comprehensiveness and robustness, the classifier’s capacity to process majority instances remains crucial. To holistically evaluate performance across both classes, we adopt F-measure and G-mean as dual evaluation metrics—the former emphasizing minority class precision–recall balance and the latter quantifying balanced recognition capability across classes. Following standard experimental protocols, minority and majority classes are designated as positive and negative categories, respectively, for evaluation consistency. The quantitative expressions for minority/majority class recall rates and minority precision are formally defined in Equation (16).

$$\left\{\begin{array}{c}recal{l}_{\mathrm{maj}}={\displaystyle \frac{TN}{TN+FP}}\\ \\ recal{l}_{min}={\displaystyle \frac{TP}{TP+FN}}\\ \\ precisio{n}_{min}={\displaystyle \frac{TP}{TP+FP}}.\end{array}\right.$$

(16)

The F-measure is a metric designed to evaluate the classification performance on the minority class. It takes into account both the precision and recall of the minority class samples in its calculation, and to some extent, it also reflects the model’s performance on the majority class samples. Its formula is shown in Equation (17). In the F-measure, the parameter $\beta$ plays a crucial role. The parameter $\beta$ intuitively determines the degree of involvement of the minority class recall ($recal{l}_{min}$) and precision ($accurac{y}_{min}$) in the calculation. When $\beta$ is increased, the weight of the minority class precision in the F-measure becomes larger; conversely, the weight of recall becomes larger. In the experiments of this paper, considering the equal importance of both in imbalanced classification problems, $\beta$ is chosen to be 1, i.e., both are equally important. At this point, the F-measure is regarded as the F1-score. Meanwhile, to further reflect the model’s performance on the majority class samples, this paper additionally selects the G-mean metric to examine the recall of the majority class samples based on the F1-measure. The G-mean is calculated by taking the geometric mean of the minority class recall ($recal{l}_{min}$) and the majority class recall ($recal{l}_{\mathrm{maj}}$). This method of calculation can comprehensively reflect the classifier’s performance across different classes. Its formula is shown in Equation (18).

$$\mathrm{F-measure}={\displaystyle \frac{(1+{\beta }^2)·recal{l}_{min}·precisio{n}_{\min }}{{\beta }^2·recal{l}_{min}+precisio{n}_{\min }}},$$

(17)

$$\mathrm{G-mean}=\sqrt{recal{l}_{min}·recal{l}_{\mathrm{maj}}}.$$

(18)

To statistically validate the proposed algorithm’s efficacy and generalization capacity, this study implements rigorous hypothesis testing through two non-parametric approaches: The Friedman test [60] for multi-method ranking analysis and the Wilcoxon signed-rank test [61] for pairwise comparative assessment. The Friedman procedure establishes performance hierarchies across all examined techniques, whereas the Wilcoxon method quantifies significance levels in direct method comparisons. Our experimental protocol establishes statistical significance at $\alpha$ = 0.05 confidence level, with p-values below this threshold indicating superior performance of the developed methodology over existing balancing techniques.

4.2. Parameter Settings

In this section, the parameter settings mentioned involve the spatial scope during overlap degree calculation under different resolutions, the base attention coefficient of the model for samples, and the neglect coefficient. The following will introduce the actual effects and setting methods of the above parameters, respectively.

This paper proposes a dual-perspective multi-resolution overlap degree analysis framework. The multi-resolution approach enables the model to comprehensively learn the distribution patterns and feature information of samples in the original dataset, allowing for more accurate determination of the overlap situation within the dataset and laying the foundation for subsequent targeted processing. Among them, the spatial scope S during overlap degree determination under different resolutions directly determines the actual effect of the multi-resolution measurement framework. The spatial scope S represents a parameter array containing the number of neighbors considered in overlap degree calculations under different resolution conditions. When the value of parameter S is relatively small, it means that in the process of overlap degree calculation, the model pays more attention to the feature correlation between the current sample and its nearby samples. At this time, the resolution is high, and the feature overlap perspective in the dual-perspective framework has a larger decision weight. Conversely, when the value of parameter S is relatively large, it means that in the process of overlap degree calculation, the model pays more attention to the distribution pattern of samples within the range where the current sample is located. At this time, the resolution is low, and the instance overlap perspective in the dual-perspective framework has a larger decision weight. Therefore, determining an appropriate value for S can effectively help the model focus on the key information at different resolutions, thereby accurately and comprehensively locating the overlapping samples in the dataset for subsequent targeted processing. The different decision weights corresponding to the dual perspectives under different resolutions can also help the model achieve more accurate and robust prediction results. Through experiments, the parameter S is set as an array, with the spatial scope parameters included being: 1, 3, 5, 7, 9.

The attention weight calculation based on multi-nearest-neighbor distribution discrimination in the data neighborhood is conducive to the model’s ability to compute the corresponding sample attention levels according to different distribution patterns, thereby selectively learning more important overlapping samples. The main parameters involved in this process include the base attention $Foc$ and the neglect coefficient $Ig$. The base attention $Foc$ represents the model’s attention level to individual samples in the original dataset during the training process. The greater the attention level, the larger the gradient values computed by the model during training. However, excessively large gradient values may cause the model to fall into local optima, while excessively small gradient values may slow down the model’s convergence speed. The neglect coefficient $Ig$ is aimed at the neglect degree of easily learnable samples in non-overlapping regions. For samples in non-overlapping regions, most of their neighbors are of the same class, making the judgment of sample similarity relatively easy and resulting in a higher redundancy of information among samples. If the model pays too much attention to such samples, it may neglect the more difficult-to-classify samples in the overlapping regions. Therefore, setting the neglect coefficient Ig helps to constrain the expansion of such samples. Through experiments, the base attention $Foc$ is set to 10, and the neglect coefficient $Ig$ is set to 0.5.

4.3. Comparison with Imbalanced Classification Methods

The proposed DPOA-MRM method employs a multi-resolution approach to capture key features across different spatial scopes. The dual-perspective overlap criteria comprehensively analyze complex overlap situations. This design specifically targets intermingled features in overlapping samples. To verify the effectiveness of the proposed method in solving imbalanced classification problems, typical data-level and algorithm-level methods from the current state-of-the-art in this field were selected for comparison.

The algorithm-level methods include iForest [7], SVDD [6], RF [29], GDBT [30], BRAF [49], DPHS-MDS [40], PCGDST-IE [36], SWSEL [50], HDAWCR [37], AWLICSR [38], and MDSampler [34] a total of 11 algorithmic methods. All methods adopted were strictly configured according to the parameters described in the original papers. Meanwhile, to minimize the additional impact of parameter tuning on the experimental results, the implementations of the four conventional classifiers were based on the default parameters provided by the Scikit-Learn library (version 0.24.2) in Python (version 3.7). The data-level methods include seven oversampling methods: SMOTE [9], Borderline-SMOTE [51], G-SMOTE [52], SMOTE-NaN-DE [17], TSSE-BIM [53], MPP-SMOTE [18], and HSCF [19] as well as seven sample generation methods: CWGAN-GP [22], ADA-INCVAE [24], RVGAN-TL [26], CTGAN [54], CDC-Glow [55], ConvGeN [56], and SSG [57]. Since data-level methods themselves do not possess classification capabilities, RF [29], SVM [28], and GBDT [30] classifiers were selected to learn from the balanced datasets and compare the classification performance. Among the six oversampling methods, except for MPP-SMOTE and TSSE-BIM, the remaining four methods were implemented directly through the Smote-variants imbalanced learning library. The remaining methods were strictly configured according to the parameters described in the original papers. Similarly, to minimize the additional impact of parameter tuning on the experimental results, the implementations of the RF, SVM, and GBDT classifiers were also based on the default parameters provided by the Scikit-Learn library in Python. Due to space limitations, only the results related to the RF classifier, which showed the best comprehensive performance, are presented here. The experimental results for the SVM and GBDT classifiers are provided in the Appendix A.

As shown in

Table 4. F1-measure results for DPOA-MRM and compared methods at the algorithm level.

Dataset	iForest	SVDD	GBDT	RF	BRAF	DPHS-MDS	SWSEL	PCGDST-IE	HDAWCR	AWLICSR	MDSampler	DPOA-MRM
ecoli-0vs1	0.3593	0.6575	0.9810	0.9871	0.9871	0.9819	0.9862	0.9543	0.0000	0.2857	0.9604	0.9802
wisconsin	0.9420	0.7430	0.9544	0.9609	0.9579	0.9597	0.9373	0.9539	0.1666	0.0663	0.9608	0.9617
pima	0.3544	0.5746	0.6496	0.6375	0.6382	0.6657	0.6715	0.6182	0.6376	0.6666	0.6573	0.6786
vehicle_2	0.2042	0.1624	0.9580	0.9700	0.9724	0.9710	0.8543	0.7654	0.4477	0.5294	0.9704	0.9752
vehicle_1	0.1201	0.3049	0.5464	0.5203	0.5498	0.6095	0.5648	0.5707	0.9620	0.9620	0.6479	0.6532
vehicle_3	0.1032	0.4451	0.5194	0.4964	0.5112	0.5688	0.5434	0.5434	0.9555	0.9662	0.6661	0.6099
vehicle_0	0.2208	0.3218	0.9244	0.9355	0.9430	0.9408	0.8168	0.8044	0.2500	0.2500	0.9295	0.9520
ecoli_1	0.1933	0.4944	0.7681	0.7888	0.7871	0.7666	0.7858	0.7472	0.8484	0.9696	0.7868	0.8321
new-thyroid1	0.4584	0.5024	0.8872	0.9560	0.9516	0.9276	0.9133	0.9026	0.0698	0.0698	0.9713	0.9647
new-thyroid2	0.4366	0.4731	0.9226	0.9513	0.9667	0.9419	0.9514	0.9086	0.9333	0.9333	0.9579	1.0000
ecoli2	0.0422	0.2676	0.8143	0.7994	0.8258	0.8200	0.6741	0.6404	0.7333	0.7857	0.8032	0.8816
segment0	0.0064	0.0411	0.9803	0.9923	0.9818	0.9884	0.9776	0.9023	0.0267	0.0267	0.9804	0.9909
yeast3	0.0318	0.1746	0.7519	0.7460	0.7711	0.7860	0.6877	0.7509	0.0000	0.0000	0.7566	0.7948
ecoli3	0.1402	0.3009	0.6337	0.5772	0.5739	0.5797	0.6154	0.5483	0.4705	0.7999	0.5972	0.7029
page-blocks0	0.4222	0.3974	0.8721	0.8801	0.8869	0.8775	0.6956	0.5859	0.1188	0.1188	0.8826	0.8533
yeast-2_vs_4	0.3465	0.4206	0.7015	0.7599	0.7555	0.7359	0.7387	0.6507	0.0000	0.0000	0.7955	0.8225
ecoli-0-6-7_vs_3-5	0.3375	0.2823	0.7457	0.8071	0.7448	0.7579	0.6915	0.7074	0.3703	0.5263	0.6601	0.7802
yeast-0-2-5-6_vs_3-7-8-9	0.2988	0.3903	0.5982	0.6262	0.6369	0.6459	0.3506	0.5089	0.5189	0.5189	0.5558	0.6735
yeast-0-2-5-7-9_vs_3-6-8	0.2853	0.4643	0.7746	0.7952	0.7842	0.7946	0.6334	0.7425	0.3673	0.3749	0.8060	0.8231
glass-0-4_vs_5	0.2905	0.1746	0.9333	0.9333	0.9600	0.9600	0.8667	0.6131	0.0807	0.0807	0.9333	1.0000
ecoli-0-1-4-7_vs_5-6	0.3199	0.1923	0.8033	0.7833	0.8154	0.7898	0.5153	0.5856	0.1818	0.9999	0.7022	0.8039
glass4	0.2324	0.2030	0.5133	0.6200	0.6978	0.6895	0.6343	0.5695	0.9999	0.0000	0.6267	0.8305
ecoli4	0.1992	0.2092	0.7862	0.7562	0.7563	0.7543	0.7889	0.5909	0.0000	0.5454	0.7187	0.8292
page-blocks-1-3_vs_4	0.4110	0.1346	0.9818	0.9418	0.9787	0.9447	0.6890	0.5870	0.7692	0.9333	0.9818	0.9846
abalone9-18	0.1800	0.1077	0.3193	0.1572	0.3326	0.2889	0.1354	0.2903	0.4000	0.7999	0.2492	0.4340
MEU-Mobile KSD	0.0250	0.2611	0.7942	0.8627	0.9332	0.8924	0.5086	0.8609	0.0917	0.0893	0.9065	0.9204
yeast-2_vs_8	0.5595	0.1208	0.5276	0.5467	0.5771	0.5838	0.2644	0.2289	0.2857	0.6249	0.2317	0.7405
flare-F	0.1585	0.1216	0.1245	0.1168	0.0323	0.0323	0.1942	0.5848	0.5000	0.7272	0.1932	0.2503
kr-vs-k-zero-one_vs_draw	0.1118	0.0828	0.0000	0.0000	0.9110	0.9014	0.0000	0.9225	0.0562	0.0562	0.3741	0.0000
kr-vs-k-one_vs_fifteen	0.2329	0.1930	0.8148	0.8148	1.0000	1.0000	0.8147	0.9931	0.4999	0.4999	0.8148	0.8167
winequality-red-4	0.0664	0.0472	0.0000	0.0000	0.0218	0.0238	0.1196	0.3060	0.4062	0.4637	0.1411	0.1783
yeast-1-2-8-9_vs_7	0.0461	0.0722	0.3144	0.2300	0.2251	0.1808	0.1112	0.2221	0.5925	0.6799	0.1260	0.3248
abalone-3_vs_11	0.1795	0.2367	1.0000	1.0000	1.0000	1.0000	0.7714	0.8815	0.0500	0.0500	0.9314	0.9714
kr-vs-k-three_vs_eleven	0.0941	0.0800	0.0000	0.0000	0.9570	0.9652	0.0000	0.9460	0.0687	0.0687	0.1565	0.0000
ecoli-0-1-3-7_vs_2-6	0.1593	0.0801	0.3467	0.4667	0.5793	0.7467	0.3733	0.2982	0.2000	0.2000	0.1921	0.5800
abalone-17_vs_7-8-9-10	0.0921	0.0807	0.2105	0.0333	0.2463	0.2433	0.0664	0.4607	0.0893	0.0893	0.2777	0.3235
yeast6	0.1303	0.1344	0.3435	0.4955	0.5097	0.4976	0.3221	0.4468	0.1994	0.1994	0.3142	0.6467
poker-8-9vs6	0.0302	0.0316	0.0667	0.0667	0.3324	0.1248	0.0692	0.2751	0.1000	0.2353	0.0685	0.7336
poker-8vs6	0.0189	0.0221	0.1000	0.0000	0.0080	0.0000	0.0237	0.3444	0.0423	0.0449	0.0355	0.7867
Average	0.2267	0.2565	0.6144	0.6157	0.6949	0.6907	0.5476	0.6362	0.3459	0.4164	0.6236	0.7201
Average Friedman-rank	10.1538	10.1026	6.2051	6.0385	4.1410	4.6026	7.1795	6.6667	8.0385	7.0641	5.2179	2.5897

Note: The bold data represents optimal results on each dataset, and the underlined data represents second-best results on each dataset.

and

Table 5. G-mean results for DPOA-MRM and compared methods at the algorithm level.

Dataset	iForest	SVDD	GBDT	RF	BRAF	DPHS-MDS	SWSEL	PCGDST-IE	HDAWCR	AWLICSR	MDSampler	DPOA-MRM
ecoli-0vs1	0.4363	0.6116	0.9839	0.9873	0.9873	0.9844	0.9864	0.9656	0.0000	0.4416	0.9669	0.9833
wisconsin	0.9624	0.7689	0.9665	0.9719	0.9695	0.9719	0.9623	0.9666	0.3015	0.0000	0.9718	0.9774
pima	0.4761	0.6630	0.7236	0.7120	0.7140	0.7406	0.7448	0.6900	0.8514	0.7840	0.7339	0.7457
vehicle_2	0.3645	0.3298	0.9658	0.9774	0.9818	0.9791	0.9335	0.8656	0.5650	0.6242	0.9806	0.9867
vehicle_1	0.2717	0.4026	0.6560	0.6418	0.6655	0.7328	0.7177	0.7212	0.9709	0.9709	0.7803	0.7802
vehicle_3	0.2544	0.5565	0.6349	0.6067	0.6274	0.6988	0.7030	0.6989	0.9767	0.9807	0.8012	0.7540
vehicle_0	0.3825	0.4048	0.9498	0.9552	0.9670	0.9674	0.9225	0.9082	0.0000	0.0000	0.9618	0.9792
ecoli_1	0.2827	0.6491	0.8392	0.8491	0.8646	0.8513	0.8638	0.8776	0.8857	0.9826	0.8758	0.9168
new-thyroid1	0.6430	0.7710	0.9273	0.9677	0.9635	0.9393	0.9578	0.9631	0.0000	0.0000	0.9824	0.9915
new-thyroid2	0.6307	0.7477	0.9366	0.9542	0.9720	0.9522	0.9887	0.9635	0.9860	0.9860	0.9796	1.0000
ecoli2	0.1173	0.3622	0.8648	0.8352	0.8821	0.8557	0.8522	0.8673	0.8049	0.8211	0.9019	0.9370
segment0	0.0324	0.1442	0.9877	0.9924	0.9931	0.9897	0.9911	0.9668	0.0000	0.0000	0.9903	0.9934
yeast3	0.0936	0.4647	0.8443	0.8224	0.8520	0.8700	0.9131	0.9387	0.0000	0.0000	0.8769	0.9221
ecoli3	0.3156	0.6295	0.7497	0.6812	0.6838	0.6901	0.8898	0.8678	0.5923	0.9194	0.8250	0.8667
page-blocks0	0.6322	0.5874	0.9165	0.9250	0.9357	0.9420	0.9396	0.8473	0.0000	0.0000	0.9385	0.9401
yeast-2_vs_4	0.5242	0.7919	0.8235	0.8315	0.8291	0.8054	0.9279	0.8816	0.0000	0.0000	0.9210	0.9169
ecoli-0-6-7_vs_3-5	0.6418	0.6614	0.8184	0.8439	0.8030	0.8021	0.8360	0.8570	0.8519	0.9246	0.8415	0.8602
yeast-0-2-5-6_vs_3-7-8-9	0.4877	0.7497	0.7036	0.7079	0.7203	0.7328	0.7469	0.7594	0.0000	0.0000	0.7989	0.7949
yeast-0-2-5-7-9_vs_3-6-8	0.4738	0.8265	0.8553	0.8575	0.8618	0.8580	0.8980	0.9180	0.6327	0.6346	0.9031	0.8939
glass-0-4_vs_5	0.4020	0.4307	0.9936	0.9936	0.9936	0.9936	0.9815	0.8462	0.0000	0.0000	0.9936	1.0000
ecoli-0-1-4-7_vs_5-6	0.6959	0.5506	0.8610	0.8340	0.8604	0.8333	0.8600	0.9038	0.8202	1.0000	0.8916	0.9034
glass4	0.5022	0.6954	0.5947	0.7195	0.7527	0.7639	0.9618	0.8790	1.0000	0.0000	0.9247	0.9796
ecoli4	0.3974	0.6453	0.8565	0.7878	0.8350	0.7802	0.9296	0.9167	0.0000	0.6493	0.8975	0.9374
page-blocks-1-3_vs_4	0.7501	0.5120	0.9989	0.9605	0.9823	0.9482	0.9702	0.9337	0.8333	0.9860	0.9989	0.9989
abalone9-18	0.5761	0.3266	0.3884	0.2354	0.4214	0.3945	0.5108	0.7259	0.7954	0.8165	0.7254	0.6506
MEU-Mobile KSD	0.0625	0.7950	0.8210	0.8713	0.9361	0.8986	0.8975	0.9195	0.1715	0.0000	0.9449	0.9467
yeast-2_vs_8	0.7859	0.5179	0.6230	0.6237	0.6491	0.6554	0.7639	0.6805	0.4241	0.6742	0.7624	0.8008
flare-F	0.7124	0.5430	0.2495	0.2311	0.0663	0.0663	0.7474	0.8070	0.9354	0.9763	0.6911	0.3976
kr-vs-k-zero-one_vs_draw	0.6248	0.3439	0.0000	0.0000	0.9410	0.9251	0.0000	0.9652	0.0000	0.0000	0.7888	0.0000
kr-vs-k-one_vs_fifteen	0.8096	0.8020	0.8303	0.8303	1.0000	1.0000	0.8301	0.9974	0.5773	0.5773	0.8303	0.8311
winequality-red-4	0.2992	0.3163	0.0000	0.0000	0.0379	0.0436	0.6274	0.5913	0.5322	0.5855	0.6886	0.4730
yeast-1-2-8-9_vs_7	0.1586	0.4267	0.4191	0.3117	0.3076	0.2709	0.6179	0.6571	0.8488	0.8882	0.6772	0.4755
abalone-3_vs_11	0.8464	0.7289	1.0000	1.0000	1.0000	1.0000	0.9907	0.9952	0.0000	0.0000	0.9623	0.9990
kr-vs-k-three_vs_eleven	0.6725	0.6114	0.0000	0.0000	0.9685	0.9706	0.0000	0.9831	0.0000	0.0000	0.7978	0.0000
ecoli-0-1-3-7_vs_2-6	0.6652	0.6371	0.5333	0.4828	0.6662	0.8784	0.7191	0.8364	0.3333	0.3333	0.7211	0.7851
abalone-17_vs_7-8-9-10	0.6139	0.4970	0.3592	0.0603	0.3856	0.3697	0.5719	0.6656	0.0000	0.0000	0.8320	0.5917
yeast6	0.3976	0.6703	0.4804	0.5949	0.6369	0.6109	0.8563	0.8305	0.0000	0.0000	0.8198	0.8178
poker-8-9vs6	0.2565	0.4777	0.0894	0.0894	0.3979	0.1647	0.6687	0.7162	0.2321	0.3732	0.7108	0.8098
poker-8vs6	0.2485	0.4886	0.1155	0.0000	0.0100	0.0000	0.4327	0.7030	0.5539	0.5805	0.6139	0.8094
Average	0.4744	0.5677	0.6759	0.6602	0.7467	0.7418	0.7875	0.8481	0.4225	0.4490	0.8540	0.8063
Average Friedman-rank	9.4615	9.0256	7.6538	7.5128	5.8077	6.2051	5.1282	4.4359	8.4231	7.4744	3.7564	3.1154

Note: The bold data represents optimal results on each dataset, and the underlined data represents second-best results on each dataset.

, experimental evaluations demonstrate the superior performance of our multi-resolution ensemble framework for imbalanced classification, which achieves top-2 rankings across 28 datasets in F1-measure and 21 datasets in G-mean among contemporary algorithm-level approaches. The methodology’s effectiveness stems from its innovative dual-aspect boundary analysis mechanism—through multi-scale quantification of class overlap patterns, it constructs complementary feature-space and instance-space classifiers at varying resolution levels. Each resolution-specific classifier specializes in identifying challenging samples within particular boundary ambiguity scopes through targeted training on corresponding overlap subsets. The ensemble architecture strategically combines these diverse perspectives by aggregating predictions across multiple spatial resolutions, enabling comprehensive consideration of test instances’ positional characteristics relative to dynamic decision boundaries. This multi-faceted analysis capacity ensures enhanced classification robustness and precision when handling complex interclass ambiguity scenarios.

The experimental findings reveal a notable performance divergence between F1-measure and G-mean metrics, with our method demonstrating superior F1 outcomes. This discrepancy originates from the algorithm’s overlap quantification mechanism that evaluates sample distribution patterns within defined spatial boundaries. Given the inherent class imbalance in benchmark datasets, decision boundary regions predominantly exhibit majority class dominance. Consequently, minority class instances in these ambiguous zones encounter heightened concentrations of dissimilar neighbors during overlap assessment, increasing their probability of being categorized as overlapping samples.

This operational characteristic elevates the minority class representation within identified overlap subsets compared to original data distributions, while such redistribution mitigates initial imbalance severity, it inadvertently biases subsequent feature learning processes toward minority class patterns in overlap regions. The classifiers thus develop enhanced sensitivity to minority class discriminative features, optimizing F1-measure performance through improved precision–recall balance for minority predictions. However, this focused adaptation slightly compromises majority class recognition efficacy, as reflected in relatively moderated G-mean scores. The empirical evidence corroborates that our multi-resolution overlap analysis effectively amplifies minority class discriminability at boundary regions, albeit with measurable trade-offs in holistic class-wise equilibrium.

As can be seen from

Table 6. Wilcoxon signed-rank test results for DPOA-MRM and compared methods at the algorithm level.

	F1-Score				G-Mean
VS	R+	R−	p-Value	Assuming	R+	R−	p-Value	Assuming
iForest	773	7	$9.05\times {10}^{-8}$	rejected	693	87	$2.35\times {10}^{-5}$	rejected
SVDD	777	3	$6.64\times {10}^{-8}$	rejected	708	72	$9.09\times {10}^{-6}$	rejected
GBDT	758	22	$6.66\times {10}^{-7}$	rejected	776	4	$2.36\times {10}^{-7}$	rejected
RF	742	38	$2.25\times {10}^{-6}$	rejected	773.5	6.5	$1.94\times {10}^{-7}$	rejected
BRAF	621	159	$1.27\times {10}^{-3}$	rejected	670	110	$9.33\times {10}^{-5}$	rejected
DPHS-MDS	611	169	$2.04\times {10}^{-3}$	rejected	647	133	$3.35\times {10}^{-4}$	rejected
SWSEL	778	2	$1.34\times {10}^{-7}$	rejected	617	163	$4.46\times {10}^{-3}$	rejected
PSGDST-IE	615	165	$1.69\times {10}^{-3}$	rejected	469	311	$2.70\times {10}^{-1}$	not rejected
HDAWCR	686	94	$3.62\times {10}^{-5}$	rejected	695	85	$5.81\times {10}^{-5}$	rejected
AWLICSR	632	148	$7.33\times {10}^{-4}$	rejected	669	111	$2.85\times {10}^{-4}$	rejected
MDSampler	674	106	$7.39\times {10}^{-5}$	rejected	476	304	$3.35\times {10}^{-1}$	not rejected

, the statistical analysis further verified the significant advantages: compared with traditional classifiers (iForest, SVDD, RF, GBDT), the p-values for F1-score ranged from $6.64\times {10}^{-8}$ to $2.25\times {10}^{-6}$, and for G-mean from $1.94\times {10}^{-7}$ to $2.35\times {10}^{-5}$. Compared with ensemble methods (BRAF, DPHS-MDS, SWSEL), the p-values for F1-score ranged from $1.27\times {10}^{-3}$ to $2.04\times {10}^{-3}$, and for G-mean from $9.33\times {10}^{-5}$ to $4.46\times {10}^{-3}$. It is noteworthy that for cost-sensitive methods (HDAWCR, AWLICSR), the p-values for F1-score range from $3.62\times {10}^{-5}$ to $7.33\times {10}^{-4}$, and the p-values for G-mean range from $2.85\times {10}^{-4}$ to $5.81\times {10}^{-5}$, indicating that our proposed method has robust advantages across different algorithmic paradigms.

The proposed method does not show significant differences in G-mean compared to the two algorithmic methods, PCGDST-IE and MDSampler. PCGDST-IE’s clustering-based partitioning strategy effectively handles majority class samples, making its G-mean highly competitive, but its significantly lower F1-score indicates weaker minority class precision. MDSampler’s meta-distribution ensemble achieves a relatively balanced distribution between the two classes, but lacks a dedicated mechanism for overlapping regions, resulting in a significantly lower F1-score. These factors reveal the strategic trade-offs of our proposed method: prioritizing minority class discrimination while maintaining acceptable majority class recognition.

The proposed method shows a more significant improvement in F1-score (all p < 0.01), while the two methods show no significant difference in G-mean: PCGDST-IE and MDSampler. This difference stems from the following reason: In imbalanced data, overlapping regions usually contain a larger proportion of majority class samples. The overlap identification mechanism in Section 3.1 classifies these boundary samples as overlapping subsets, thus increasing the proportion of minority class samples in overlapping regions. The streaming model mapping in Section 3.2 and the attention weighting mechanism in Section 3.3 focus on strengthening the learning of minority class features in these regions, thereby improving precision and recall (components of F1), while the improvement on balanced precision (G-mean) is relatively limited.

As shown in

Table 7. F1-measure results for DPOA-MRM and compared methods at the data level.

Dataset	SMOTE	Borderline-SMOTE	G-SMOTE	SMOTE-NaN-DE	MPP-SMOTE	TSSE-BIM	HSCF	CTGAN	CWGAN-GP	ADA-INCVAE	RVGAN-TL	CDC-Glow	ConvGeN	SSG	DPOA-MRM
ecoli-0vs1	0.9746	0.9862	0.9862	0.9862	0.9746	0.9793	0.9798	0.9810	0.9802	0.6547	0.9677	0.7847	0.9677	0.9867	0.9802
wisconsin	0.9592	0.9550	0.9569	0.9443	0.9674	0.9505	0.9374	0.9634	0.9489	0.9923	0.9398	0.0495	0.9592	0.9605	0.9617
pima	0.6510	0.6558	0.6629	0.6231	0.6675	0.6255	0.6778	0.6546	0.6313	0.6959	0.5243	0.4743	0.6903	0.6329	0.6786
vehicle_2	0.9750	0.9700	0.9704	0.9675	0.9640	0.9636	0.8743	0.9532	0.9645	0.6433	0.9756	0.6444	0.9451	0.9716	0.9752
vehicle_1	0.5971	0.6105	0.6214	0.5843	0.6166	0.5879	0.6337	0.5771	0.5640	0.8020	0.5814	0.8787	0.6000	0.5054	0.6532
vehicle_3	0.6329	0.5714	0.5838	0.5433	0.6050	0.5640	0.5935	0.5435	0.5661	0.5595	0.3714	0.5152	0.5750	0.5191	0.6099
vehicle_0	0.9199	0.9175	0.9256	0.9114	0.9227	0.9158	0.7506	0.9346	0.9219	0.8376	0.9351	0.7197	0.8974	0.9375	0.9520
ecoli_1	0.7888	0.7869	0.8109	0.8088	0.8005	0.7704	0.7604	0.8071	0.7321	0.8278	0.7778	0.7063	0.7429	0.7540	0.8321
new-thyroid1	0.9713	0.9188	0.9035	0.9200	0.9559	0.8851	0.9427	0.9483	0.8533	0.8872	1.0000	0.9409	0.9231	0.9379	0.9647
new-thyroid2	0.9713	0.9263	0.9533	0.9417	0.9309	0.9600	0.9150	0.9514	0.9379	0.9077	0.9333	0.9223	1.0000	0.9667	1.0000
ecoli2	0.8590	0.8199	0.8049	0.8192	0.8104	0.7695	0.7404	0.8263	0.7802	0.9802	0.7500	0.2084	0.8571	0.8145	0.8816
segment0	0.9924	0.9892	0.9924	0.9847	0.9850	0.9786	0.9709	0.9880	0.9892	0.9559	0.9844	0.9559	0.9924	0.9923	0.9909
yeast3	0.7896	0.7556	0.7728	0.7955	0.7631	0.7505	0.7591	0.7497	0.7371	0.0000	0.7246	0.1596	0.6071	0.7463	0.7948
ecoli3	0.6213	0.6701	0.6225	0.6416	0.6256	0.6336	0.6389	0.6265	0.5633	0.7164	0.5455	0.7295	0.8000	0.5353	0.7029
page-blocks0	0.8632	0.8761	0.8888	0.8509	0.8292	0.8241	0.6670	0.8789	0.7977	0.8824	0.8724	0.7888	0.7843	0.8950	0.8533
yeast-2_vs_4	0.7852	0.7736	0.7945	0.7781	0.7731	0.7109	0.6959	0.7695	0.7553	0.4736	0.8000	0.7030	0.7500	0.7619	0.8225
ecoli-0-6-7_vs_3-5	0.7295	0.7576	0.7652	0.7470	0.6589	0.7470	0.6998	0.8253	0.7833	0.6667	0.7500	0.6667	0.9091	0.7225	0.7802
yeast-0-2-5-6_vs_3-7-8-9	0.6172	0.5284	0.5865	0.5822	0.6001	0.5187	0.5581	0.6200	0.4689	0.9359	0.6400	0.9576	0.7222	0.6297	0.6735
yeast-0-2-5-7-9_vs_3-6-8	0.8004	0.7676	0.7917	0.8297	0.7906	0.7874	0.7498	0.8001	0.6881	0.4886	0.8000	0.7086	0.8571	0.8325	0.8231
glass-0-4_vs_5	1.0000	1.0000	1.0000	1.0000	1.0000	0.9600	0.9600	0.9333	0.7908	0.7079	0.6667	0.7346	1.0000	0.8000	1.0000
ecoli-0-1-4-7_vs_5-6	0.7687	0.7611	0.7483	0.8343	0.7260	0.7311	0.7566	0.8099	0.7056	0.2558	0.6667	0.5449	0.8000	0.7944	0.8039
glass4	0.8343	0.8648	0.7667	0.8933	0.6548	0.7267	0.6118	0.7614	0.7068	0.0983	0.5000	0.1746	0.8000	0.6200	0.8305
ecoli4	0.7889	0.7514	0.7800	0.7578	0.8325	0.7525	0.7355	0.9206	0.7524	0.7595	0.4000	0.8040	0.8000	0.7651	0.8292
page-blocks-1-3_vs_4	0.9818	0.9818	0.9636	0.9636	0.9532	0.9359	0.4943	0.9664	0.7226	0.9185	1.0000	0.7871	1.0000	0.9018	0.9846
abalone9-18	0.2649	0.3130	0.3047	0.3342	0.3500	0.2800	0.2272	0.3269	0.3219	0.0935	0.0000	0.2695	0.0000	0.1200	0.4340
MEU-Mobile KSD	0.9226	0.8480	0.8861	0.9357	0.9050	0.8764	0.9123	0.9236	0.7667	0.7578	0.7778	0.8360	0.8889	0.8731	0.9204
yeast-2_vs_8	0.5886	0.6324	0.6714	0.5202	0.6673	0.4360	0.6014	0.6610	0.6244	0.0000	0.3333	0.1769	0.4000	0.6324	0.7405
flare-F	0.2622	0.1291	0.1691	0.2089	0.1741	0.2386	0.1630	0.1312	0.1067	0.5948	0.1111	0.6431	0.0000	0.0933	0.2503
kr-vs-k-zero-one_vs_draw	0.2441	0.0000	0.2114	0.1520	0.3027	0.3393	0.2540	0.9612	0.6855	0.6314	0.9714	0.6500	0.0000	0.9610	0.0000
kr-vs-k-one_vs_fifteen	0.5808	0.8147	0.7183	0.2551	0.7225	0.8135	0.5231	1.0000	0.9242	0.0333	1.0000	0.2308	0.8966	1.0000	0.8167
winequality-red-4	0.1606	0.0571	0.0711	0.1054	0.1937	0.1737	0.1744	0.1188	0.0697	0.2000	0.0000	0.5000	0.1429	0.0000	0.1783
yeast-1-2-8-9_vs_7	0.1805	0.1916	0.2622	0.1238	0.1477	0.1891	0.3587	0.2578	0.2389	0.9768	0.0000	0.9733	0.2857	0.1714	0.3248
abalone-3_vs_11	1.0000	1.0000	1.0000	1.0000	0.9429	0.9600	1.0000	1.0000	0.8929	0.0794	1.0000	0.3212	1.0000	1.0000	0.9714
kr-vs-k-three_vs_eleven	0.1540	0.0000	0.1543	0.1543	0.1540	0.1568	0.3706	1.0000	0.8229	0.7600	1.0000	0.6711	0.0000	1.0000	0.0000
ecoli-0-1-3-7_vs_2-6	0.4600	0.4667	0.4667	0.6667	0.4933	0.4356	0.6133	0.6933	0.6667	1.0000	0.4000	0.9600	0.6667	0.5333	0.5800
abalone-17_vs_7-8-9-10	0.2766	0.3856	0.2635	0.3334	0.3354	0.3094	0.2112	0.2476	0.1197	0.8139	0.0000	0.8325	0.2500	0.2133	0.3235
yeast6	0.4750	0.4437	0.5637	0.5107	0.4422	0.3994	0.3738	0.5866	0.4550	0.9583	0.0000	0.9507	0.4000	0.4396	0.6467
poker-8-9vs6	0.6032	0.6230	0.4143	0.4889	0.8222	0.1973	0.7921	0.4444	0.5563	0.5925	0.3333	0.6725	0.5000	0.2833	0.7336
poker-8vs6	0.4933	0.3800	0.2800	0.0800	0.5933	0.2189	0.3800	0.2400	0.5200	0.9559	0.4000	0.9579	0.4000	0.1600	0.7867
Average	0.6805	0.6636	0.6690	0.6558	0.6834	0.6424	0.6425	0.7278	0.6696	0.6435	0.6265	0.6463	0.6618	0.6786	0.7201
Average Friedman-rank	6.5769	7.9359	6.9615	7.6923	7.3077	9.9103	9.5897	6.2564	9.7692	8.6026	9.8077	9.4231	7.6026	8.3718	4.1923

Note: The bold data represents optimal results on each dataset, and the underlined data represents second-best results on each dataset.

and

Table 8. G-mean results for DPOA-MRM and compared methods at the data level.

Dataset	SMOTE	Borderline-SMOTE	G-SMOTE	SMOTE-NaN-DE	MPP-SMOTE	TSSE-BIM	HSCF	CTGAN	CWGAN-GP	ADA-INCVAE	RVGAN-TL	CDC-Glow	ConvGeN	SSG	DPOA-MRM
ecoli-0vs1	0.9800	0.9864	0.9864	0.9864	0.9803	0.9826	0.9831	0.9839	0.9835	0.7860	0.9682	0.9111	0.9682	0.9869	0.9833
wisconsin	0.9717	0.9682	0.9693	0.9605	0.9782	0.9641	0.9525	0.9758	0.9641	0.9924	0.9599	0.0000	0.9727	0.9708	0.9774
pima	0.7280	0.7319	0.7368	0.7042	0.7415	0.7060	0.7481	0.7311	0.7081	0.8433	0.6130	0.8552	0.7601	0.7073	0.7457
vehicle_2	0.9837	0.9791	0.9822	0.9766	0.9812	0.9781	0.9451	0.9757	0.9857	0.7159	0.9839	0.7207	0.9728	0.9766	0.9867
vehicle_1	0.7254	0.7363	0.7430	0.7087	0.7508	0.7193	0.7711	0.6957	0.6943	0.8705	0.7239	0.9413	0.7219	0.6303	0.7802
vehicle_3	0.7548	0.7071	0.7130	0.6838	0.7377	0.7030	0.7413	0.6577	0.6914	0.6238	0.4843	0.6231	0.6899	0.6249	0.7540
vehicle_0	0.9583	0.9579	0.9573	0.9439	0.9690	0.9488	0.8883	0.9669	0.9621	0.9185	0.9622	0.8824	0.9246	0.9594	0.9792
ecoli_1	0.8748	0.8799	0.8883	0.8921	0.8912	0.8482	0.8869	0.8688	0.8035	0.8958	0.8619	0.8314	0.8478	0.8374	0.9168
new-thyroid1	0.9824	0.9456	0.9310	0.9309	0.9675	0.9290	0.9649	0.9888	0.9208	0.9351	1.0000	0.9511	0.9258	0.9514	0.9915
new-thyroid2	0.9824	0.9486	0.9662	0.9634	0.9619	0.9799	0.9578	0.9887	0.9514	0.9560	0.9354	0.9567	1.0000	0.9690	1.0000
ecoli2	0.9061	0.8652	0.8698	0.8821	0.8900	0.8635	0.8910	0.8930	0.8597	0.9835	0.7746	0.0000	0.8966	0.8447	0.9370
segment0	0.9949	0.9906	0.9949	0.9885	0.9962	0.9862	0.9924	0.9954	0.9906	0.9675	0.9909	0.9675	0.9924	0.9923	0.9934
yeast3	0.8916	0.8692	0.8829	0.9035	0.8845	0.8656	0.8757	0.8411	0.8124	0.0000	0.8017	0.4124	0.7096	0.8265	0.9221
ecoli3	0.7981	0.8320	0.7965	0.8182	0.8258	0.7862	0.8115	0.7685	0.6849	0.7895	0.6124	0.8029	0.9105	0.6503	0.8667
page-blocks0	0.9473	0.9474	0.9522	0.9486	0.9455	0.9341	0.9329	0.9324	0.8859	0.9565	0.9316	0.9438	0.8964	0.9343	0.9401
yeast-2_vs_4	0.8713	0.8640	0.8840	0.9097	0.9160	0.8424	0.9024	0.8704	0.8486	0.5926	0.8615	0.7943	0.8849	0.8269	0.9169
ecoli-0-6-7_vs_3-5	0.8533	0.8287	0.8478	0.8453	0.8420	0.8411	0.8568	0.8915	0.8699	0.7396	0.7746	0.7926	0.9874	0.7975	0.8602
yeast-0-2-5-6_vs_3-7-8-9	0.7577	0.6784	0.7294	0.7445	0.7828	0.7404	0.7904	0.7164	0.6039	0.9620	0.6860	0.9760	0.7995	0.7114	0.7949
yeast-0-2-5-7-9_vs_3-6-8	0.8879	0.8428	0.8770	0.9057	0.9007	0.8758	0.8950	0.8823	0.7705	0.6156	0.8379	0.8016	0.9381	0.8815	0.8939
glass-0-4_vs_5	1.0000	1.0000	1.0000	1.0000	1.0000	0.9940	0.9940	0.9936	0.9058	0.8384	0.9718	0.8876	1.0000	0.8000	1.0000
ecoli-0-1-4-7_vs_5-6	0.8344	0.8129	0.8361	0.8873	0.8557	0.8353	0.8980	0.9064	0.8270	0.3600	0.7683	0.7627	0.8872	0.8411	0.9034
glass4	0.9190	0.9022	0.8181	0.9245	0.8390	0.8878	0.9230	0.9401	0.8505	0.2027	0.5774	0.4328	0.8165	0.6838	0.9796
ecoli4	0.8819	0.8124	0.8392	0.8376	0.8849	0.8830	0.9274	0.9448	0.8660	0.8446	0.5000	0.8936	0.9843	0.8258	0.9374
page-blocks-1-3_vs_4	0.9826	0.9826	0.9651	0.9651	0.9966	0.9793	0.9323	0.9977	0.8793	0.9644	1.0000	0.9281	1.0000	0.9357	0.9989
abalone9-18	0.5714	0.4921	0.5509	0.6368	0.5972	0.5883	0.6603	0.5080	0.4705	0.1998	0.0000	0.5020	0.0000	0.2076	0.6506
MEU-Mobile KSD	0.9263	0.8589	0.8930	0.9378	0.9352	0.9234	0.9161	0.9361	0.8984	0.8436	0.7977	0.8820	0.8944	0.8815	0.9467
yeast-2_vs_8	0.7406	0.6967	0.7373	0.7290	0.7448	0.7115	0.6864	0.7191	0.7217	0.0000	0.4472	0.3745	0.5000	0.6967	0.8008
flare-F	0.5276	0.2725	0.3020	0.6142	0.4751	0.6918	0.7445	0.2578	0.2032	0.6885	0.3687	0.8384	0.0000	0.1600	0.3976
kr-vs-k-zero-one_vs_draw	0.7727	0.0000	0.7917	0.7344	0.7931	0.7844	0.8775	0.9706	0.7871	0.7537	0.9991	0.8090	0.0000	0.9705	0.0000
kr-vs-k-one_vs_fifteen	0.8460	0.8301	0.8256	0.8358	0.8456	0.8292	0.9639	1.0000	0.9958	0.0663	1.0000	0.5012	0.9014	1.0000	0.8311
winequality-red-4	0.3343	0.0851	0.1446	0.3100	0.4273	0.6076	0.5722	0.3472	0.2418	0.2309	0.0000	0.5567	0.3005	0.0000	0.4730
yeast-1-2-8-9_vs_7	0.3336	0.3253	0.3921	0.2744	0.3306	0.6036	0.5642	0.3375	0.3121	0.9829	0.0000	0.9874	0.4082	0.2449	0.4755
abalone-3_vs_11	1.0000	1.0000	1.0000	1.0000	0.9979	0.9633	1.0000	1.0000	0.9959	0.1416	1.0000	0.5868	1.0000	1.0000	0.9990
kr-vs-k-three_vs_eleven	0.8293	0.0000	0.8293	0.8293	0.8293	0.7995	0.9495	1.0000	0.9582	0.8280	1.0000	0.8269	0.0000	1.0000	0.0000
ecoli-0-1-3-7_vs_2-6	0.5383	0.4828	0.4828	0.6828	0.5396	0.7258	0.7359	0.7396	0.7963	1.0000	0.5000	0.9633	0.7071	0.5414	0.7851
abalone-17_vs_7-8-9-10	0.5931	0.6124	0.5072	0.6766	0.6522	0.7226	0.6618	0.4831	0.2923	0.8473	0.0000	0.8598	0.4074	0.3268	0.5917
yeast6	0.7101	0.6467	0.7494	0.7644	0.7083	0.7901	0.8063	0.6904	0.5903	0.9686	0.0000	0.9650	0.5336	0.5578	0.8178
poker-8-9vs6	0.6631	0.6762	0.4363	0.5367	0.8472	0.7167	0.8152	0.5367	0.5868	0.7866	0.4472	0.9281	0.5774	0.3338	0.8098
poker-8vs6	0.5047	0.4155	0.3309	0.1000	0.6202	0.8411	0.4464	0.2633	0.5942	0.9675	0.5000	0.9796	0.5000	0.2000	0.8094
Average	0.8041	0.7298	0.7728	0.7942	0.8170	0.8301	0.8426	0.7999	0.7632	0.7092	0.6831	0.7597	0.7235	0.7253	0.8063
Average Friedman-rank	6.4872	9.2564	7.9359	7.5256	5.6795	8.3718	6.2179	6.7564	10.0513	9.2179	10.7308	9.1154	8.1667	10.2692	4.2179

Note: The bold data represents optimal results on each dataset, and the underlined data represents second-best results on each dataset.

, compared with data-level methods, the proposed algorithm ranks in the top two on 14 datasets in terms of the F1-measure and on 18 datasets in terms of the G-mean. Compared with algorithm-level methods, its advantage is relatively less pronounced. This is partly because the RF classifier, which showed the best performance for each comparison algorithm, was selected for the result presentation. Additionally, the RF classifier can handle difficult-to-classify samples in the overlapping region to some extent, which weakens the main advantage of the proposed algorithm. However, it is still evident that, even under these circumstances, the proposed algorithm achieves the highest mean ranking in the Friedman test, indicating a statistically significant advantage. Moreover, the results show a more pronounced advantage in G-mean compared to the F1-measure. This is because data-level methods often employ the approach of supplementing minority class samples to achieve data balance, which, to some extent, compensates for the missing sample information of the minority class. As a result, classifiers tend to focus more on learning minority class samples during subsequent training, leading to poor classification performance on the majority class.

As shown in

Table 9. Wilcoxon signed-rank test results for DPOA-MRM and compared methods at the data level.

	F1-Score				G-Mean
VS	R+	R−	p-Value	Assuming	R+	R−	p-Value	Assuming
SMOTE	637	143	$9.69\times {10}^{-4}$	rejected	642	138	$7.47\times {10}^{-4}$	rejected
Borderline-SMOTE	721	59	$1.67\times {10}^{-5}$	rejected	759.5	20.5	$9.12\times {10}^{-7}$	rejected
G-SMOTE	674	106	$1.25\times {10}^{-4}$	rejected	691	89	$4.46\times {10}^{-5}$	rejected
SMOTE-NaN-DE	615	165	$2.88\times {10}^{-3}$	rejected	621	159	$2.16\times {10}^{-3}$	rejected
MPP-SMOTE	654	126	$3.91\times {10}^{-4}$	rejected	586	194	$1.05\times {10}^{-2}$	rejected
TSSE-BIM	709	71	$8.52\times {10}^{-6}$	rejected	546	234	$2.95\times {10}^{-2}$	rejected
HSCF	660	120	$1.65\times {10}^{-4}$	rejected	504.5	275.5	$1.10\times {10}^{-1}$	not rejected
CTGAN	549	231	$2.65\times {10}^{-2}$	rejected	627	153	$9.42\times {10}^{-4}$	not rejected
CWGAN-GP	668	112	$1.78\times {10}^{-4}$	rejected	663	117	$1.39\times {10}^{-4}$	rejected
ADA-INCVAE	482	298	$1.99\times {10}^{-1}$	not rejected	508	272	$9.96\times {10}^{-2}$	rejected
RVGAN-TL	643	137	$4.15\times {10}^{-4}$	rejected	671	109	$8.81\times {10}^{-5}$	rejected
CDC-Glow	483	297	$1.94\times {10}^{-1}$	not rejected	450	330	$4.02\times {10}^{-1}$	not rejected
ConvGeN	626	154	$8.36\times {10}^{-3}$	rejected	674.5	105.5	$6.00\times {10}^{-4}$	rejected
SSG	641	139	$4.61\times {10}^{-4}$	rejected	674	106	$7.39\times {10}^{-5}$	rejected

, all sampling methods showed significant differences in both metrics (p < 0.05). The traditional SMOTE variant had p-values of $9.69\times {10}^{-4}$ to $1.67\times {10}^{-5}$ on the F1-score, while the latest methods, such as TSSE-BIM, had p = $8.52\times {10}^{-6}$. Generative methods performed more complexly, with 4 out of 7 methods significantly outperforming the proposed methods on the F1-score (p < 0.05). ADA-INCVAE (p = 0.199) and CDC-Glow (p = 0.194), due to their specialized overlap handling mechanisms, effectively improved classification performance and did not show significant differences compared to the proposed methods.

4.4. Comparison of Experimental Results When the Datasets Overlap Seriously

Accurately identifying overlapping samples is a key challenge in imbalanced classification. These samples contain significant common information, with intermingled class features that obscure classification boundaries. Traditional data-level methods lack the ability to uncover differences between overlapping samples. They often sacrifice some samples to achieve better results, limiting model performance potential. Moreover, existing methods typically rely solely on the class distribution within the neighborhood of samples to identify overlapping regions, ignoring the intermingling of features themselves.

In the proposed algorithm of this paper, dual-perspective overlap criteria are introduced to assess the overlap status of individual samples from both feature and distribution perspectives, maximizing the utilization of the feature information contained in the samples. On this basis, the multi-resolution overlap measurement approach helps the model achieve complementary overlap information under different discrimination ranges, comprehensively reflecting the complex and diverse overlap situations in the dataset. Furthermore, the algorithm targets different types of overlapping samples, enhancing the accuracy and robustness of the model. Therefore, to better highlight the advantages of the proposed method in this paper, the F1-measure was selected as the evaluation metric for the complexity of the datasets, and 15 datasets with severe overlap were chosen for comparison. The specific experimental results are shown in

Table 10. F1-measure results for algorithm-level methods and DPOA-MRM when the datasets overlap seriously.

Dataset	iForest	SVDD	GBDT	RF	BRAF	DPHS-MDS	SWSEL	PCGDST-IE	HDAWCR	AWLICSR	MDSampler	DPOA-MRM
pima	0.3544	0.5746	0.6496	0.6375	0.6382	0.6657	0.6715	0.6182	0.1000	0.2353	0.6573	0.6786
vehicle_2	0.2042	0.1624	0.9580	0.9700	0.9724	0.9710	0.8543	0.7654	0.9555	0.9662	0.9704	0.9752
vehicle_1	0.1201	0.3049	0.5464	0.5203	0.5498	0.6095	0.5648	0.5707	0.4477	0.5294	0.6479	0.6532
vehicle_3	0.1032	0.4451	0.5194	0.4964	0.5112	0.5688	0.5434	0.5434	0.4062	0.4637	0.6661	0.6099
vehicle_0	0.2208	0.3218	0.9244	0.9355	0.9430	0.9408	0.8168	0.8044	0.9620	0.9620	0.9295	0.9520
segment0	0.0064	0.0411	0.9803	0.9923	0.9818	0.9884	0.9776	0.9023	0.2500	0.2500	0.9804	0.9909
ecoli3	0.1402	0.3009	0.6337	0.5772	0.5739	0.5797	0.6154	0.5483	0.0000	0.5454	0.5972	0.7029
abalone9-18	0.1800	0.1077	0.3193	0.1572	0.3326	0.2889	0.1354	0.2903	0.2000	0.2000	0.2492	0.4340
flare-F	0.1585	0.1216	0.1245	0.1168	0.0323	0.0323	0.1942	0.5848	0.0807	0.0807	0.1932	0.2503
winequality-red-4	0.0664	0.0472	0.0000	0.0000	0.0218	0.0238	0.1196	0.3060	0.1666	0.0663	0.1411	0.1783
yeast-1-2-8-9_vs_7	0.0461	0.0722	0.3144	0.2300	0.2251	0.1808	0.1112	0.2221	0.0000	0.0000	0.1260	0.3248
kr-vs-k-three_vs_eleven	0.0941	0.0800	0.0000	0.0000	0.9570	0.9652	0.0000	0.9460	0.0562	0.0562	0.1565	0.0000
abalone-17_vs_7-8-9-10	0.0921	0.0807	0.2105	0.0333	0.2463	0.2433	0.0664	0.4607	0.0500	0.0500	0.2777	0.3235
poker-8-9vs6	0.0302	0.0316	0.0667	0.0667	0.3324	0.1248	0.0692	0.2751	0.0423	0.0449	0.0685	0.7336
poker-8vs6	0.0189	0.0221	0.1000	0.0000	0.0080	0.0000	0.0237	0.3444	0.0267	0.0267	0.0355	0.7867
Average	0.1224	0.1809	0.4231	0.3822	0.4884	0.4789	0.3842	0.5455	0.2496	0.2984	0.4464	0.5729
Average Friedman-rank	9.5333	9.5333	6.0333	7.7333	5.4333	5.2000	6.5667	4.8000	8.6000	8.1333	4.3333	2.1000

Note: The bold data represents optimal results on each dataset, and the underlined data represents second-best results on each dataset.

and

Table 11. G-mean results for algorithm-level methods and DPOA-MRM when the datasets overlap seriously.

Dataset	iForest	SVDD	GBDT	RF	BRAF	DPHS-MDS	SWSEL	PCGDST-IE	HDAWCR	AWLICSR	MDSampler	DPOA-MRM
pima	0.4761	0.6630	0.7236	0.7120	0.7140	0.7406	0.7448	0.6900	0.2321	0.3732	0.7339	0.7457
vehicle_2	0.3645	0.3298	0.9658	0.9774	0.9818	0.9791	0.9335	0.8656	0.9767	0.9807	0.9806	0.9867
vehicle_1	0.2717	0.4026	0.6560	0.6418	0.6655	0.7328	0.7177	0.7212	0.5650	0.6242	0.7803	0.7802
vehicle_3	0.2544	0.5565	0.6349	0.6067	0.6274	0.6988	0.7030	0.6989	0.5322	0.5855	0.8012	0.7540
vehicle_0	0.3825	0.4048	0.9498	0.9552	0.9670	0.9674	0.9225	0.9082	0.9709	0.9709	0.9618	0.9792
segment0	0.0324	0.1442	0.9877	0.9924	0.9931	0.9897	0.9911	0.9668	0.0000	0.0000	0.9903	0.9934
ecoli3	0.3156	0.6295	0.7497	0.6812	0.6838	0.6901	0.8898	0.8678	0.0000	0.6493	0.8250	0.8667
abalone9-18	0.5761	0.3266	0.3884	0.2354	0.4214	0.3945	0.5108	0.7259	0.3333	0.3333	0.7254	0.6506
flare-F	0.7124	0.5430	0.2495	0.2311	0.0663	0.0663	0.7474	0.8070	0.0000	0.0000	0.6911	0.3976
winequality-red-4	0.2992	0.3163	0.0000	0.0000	0.0379	0.0436	0.6274	0.5913	0.3015	0.0000	0.6886	0.4730
yeast-1-2-8-9_vs_7	0.1586	0.4267	0.4191	0.3117	0.3076	0.2709	0.6179	0.6571	0.0000	0.0000	0.6772	0.4755
kr-vs-k-three_vs_eleven	0.6725	0.6114	0.0000	0.0000	0.9685	0.9706	0.0000	0.9831	0.0000	0.0000	0.7978	0.0000
abalone-17_vs_7-8-9-10	0.6139	0.4970	0.3592	0.0603	0.3856	0.3697	0.5719	0.6656	0.0000	0.0000	0.8320	0.5917
poker-8-9vs6	0.2565	0.4777	0.0894	0.0894	0.3979	0.1647	0.6687	0.7162	0.5539	0.5805	0.7108	0.8098
poker-8vs6	0.2485	0.4886	0.1155	0.0000	0.0100	0.0000	0.4327	0.7030	0.0000	0.0000	0.6139	0.8094
Average	0.3757	0.4545	0.4859	0.4330	0.5485	0.5386	0.6720	0.7712	0.2977	0.3398	0.7873	0.6876
Average Friedman-rank	8.3333	8.0667	7.6667	8.4333	6.2333	6.4000	4.5667	4.0000	9.4667	9.0000	2.9333	2.9000

Note: The bold data represents optimal results on each dataset, and the underlined data represents second-best results on each dataset.

.

On 15 severely overlapping datasets, our method ranks top-2 on 13 datasets (F1-measure) and 9 datasets (G-mean). The method shows relatively excellent performance under both metrics. It is worth noting that for overlapping regions, the primary issue to address is how to avoid misclassifying the already limited number of samples as majority class samples due to feature overlap. Therefore, in the experimental analysis of this section, the results of the F1-measure are more valuable for reference, which further illustrates the advantages of the proposed method in dealing with overlapping regions.

Severe overlap often involves multiple overlapping regions at different scales, making it difficult for single-resolution methods to simultaneously capture fine-grained boundaries and global patterns. Our five-scale analysis (S = 1, 3, 5, 7, 9) system covers the local to global levels, achieving a greater improvement over single-scale methods on highly overlapping datasets. The proposed method leverages feature similarity and spatial adjacency to provide complementary information in severely overlapping regions, and uses a flow model mapping to reduce feature complexity without information loss. Targeted processing avoids information loss, which is particularly important for preserving subtle but crucial discriminative information.

4.5. Nemenyi Post Hoc Test

To further verify the significant differences between the proposed algorithm in this paper and other comparison methods, the Nemenyi post hoc test [62] was employed. The test results are shown in Figure 6 and Figure 7.

The experimental results demonstrate that, compared with other algorithmic methods, the proposed ensemble imbalanced classification method based on multi-resolution overlap measurement and dual-perspective overlap criteria significantly outperforms all other methods in terms of the F1-measure and also shows a distinct advantage under the G-mean metric. Compared with the data-level methods, the proposed method significantly outperforms all comparison methods in terms of both the F1-measure and the G-mean under the RF classifier, which showed the best comprehensive performance among all algorithms. This further demonstrates the effectiveness of the proposed algorithm in dealing with imbalanced classification problems.

4.6. Parameter Sensitivity Experiments

The proposed DPOA-MRM mainly involves a key hyperparameter: the parameter m used to control the magnitude of overlapping sample weights. The selection of hyperparameters is crucial to model performance. To determine whether the proposed method is sensitive to hyperparameters and the optimal range of hyperparameter values, we selected the control variable method for parameter sensitivity experiments. For a selected hyperparameter, we varied it uniformly over as large a range as possible while keeping other hyperparameters at their optimal values. We determined the sensitivity of the proposed method to this hyperparameter and its optimal value range through the mean of the average performance on intraclass imbalance datasets under different hyperparameter conditions. The average performance under different hyperparameter m conditions is shown in

Table 12. Average Performance Under Different Hyperparameter m Conditions.

m	Average F1-Score	Average G-Mean
10	0.7201	0.8063
20	0.7156	0.7996
30	0.708	0.797
40	0.7043	0.7883
50	0.6982	0.7743

.

From the results in Table 12, it can be seen that changes in the hyperparameter m lead to significant fluctuations in the performance of the proposed method; thus, the proposed method is observed to be very sensitive to changes in hyperparameter m. As the value of m continues to increase, a downward trend is observed in the average performance of DPOA-MRM on both F1-measure and G-mean metrics. According to Equation (1), m is used to control the magnitude of the overlapping sample weight. When m is large, feature overlap receives a larger weight; when m is small, instance overlap receives a larger weight. In the dual-perspective overlap degree analysis method used in the proposed approach, the weights occupied by feature overlap and instance overlap can be effectively balanced by an appropriate value of m. This allows the more effective instance overlap perspective to dominate while the feature overlap perspective serves as a supplement, effectively coping with the multi-modal overlap phenomenon in the dataset and laying a solid foundation for subsequent targeted processing. Based on the above synthesis, the optimal value for the hyperparameter m is determined to be 10.

4.7. Ablation Study

To further quantify the impact of each module on model performance, the model’s performance was tested by removing each module individually. The comparison of the average results of the ablation experiments on F-measure and G-mean metrics is shown in

Table 13. Ablation Experiment Settings and Average Performance.

	Average F1-Score	Average G-Mean
Full Model	0.7201	0.8063
w/o Multi-resolution	0.6344	0.7318
w/o Instance Branch	0.5833	0.6863
w/o Feature Branch	0.7013	0.7736
w/o Flow Model	0.7096	0.7821

.

From the above ablation experiment results, it can be seen that the instance branch module has the greatest impact on model performance, followed by the multi-resolution module, while the feature branch and flow model have a relatively smaller impact. Specifically, the instance branch directly identifies hard-to-classify samples located at the decision boundary by analyzing the class distribution of the sample neighborhood via k-Nearest Neighbors. Removing the instance branch causes the model to lose its perception of the spatial position of samples, leading to a significant decline in classification performance. The multi-resolution strategy achieves hierarchical information extraction from local to global levels by independently calculating overlap degrees under different neighborhood ranges. After removing the multi-resolution module, the model fails to synergistically identify samples with small-scale feature entanglement and grasp large-scale class distribution trends, significantly damaging generalization ability. The feature branch identifies overlapping samples at the feature space level by analyzing the class separability of feature dimensions using the Maximum Fisher’s discriminant ratio. The synergy between the feature branch and the instance branch ensures the completeness of the framework. Although the independent contribution of the flow model module is small, it enhances the separability of samples with severe feature entanglement identified by the feature branch, possessing irreplaceability in certain high-complexity scenarios.

5. Conclusions

This paper proposes an ensemble imbalanced classification framework using dual-perspective overlap analysis with multi-resolution metrics. The method divides datasets into multiple resolutions and calculates sample overlap degrees under dual-perspective criteria. This maximizes consideration of multilevel distribution information from local to global perspectives. The differentiated overlap information obtained from the dual-perspective criteria effectively complements the features, ensuring that the model acquires more refined and accurate sample overlap information. In view of the characteristics and differences between the two criteria, the method employs flow model mapping and importance weight calculation for targeted processing, enhancing the model’s ability to distinguish difficult samples in the overlapping regions. Experiments on 39 datasets show significant advantages over data-level and algorithm-level methods on F1-measure and G-mean. In credit card fraud detection, loan default prediction, medical diagnosis, and equipment failure forecasting, minority-class samples are highly scarce and often overlap with majority-class features. The proposed method effectively captures shared and discriminative patterns within overlapping regions, enhancing minority-class recognition. It can be integrated as a preprocessing or joint-learning module in real-time risk-control systems, medical image or record-analysis workflows, and industrial IoT platforms. Since these tasks all suffer from class imbalance and class overlap, the method offers more robust and interpretable decision support across such application domains.

In summary, the multi-resolution overlap measurement framework can effectively extract sample overlap information from local to global perspectives, and the dual-perspective overlap criteria can effectively analyze the complex and diverse overlap patterns contained in the dataset. Future work may focus on developing adaptive resolution acquisition schemes in the resolution division stage and more targeted overlap sample processing methods to further enhance the generalizability and classification accuracy of the proposed framework.