To address the issues of high computational overhead and the inability to capture hierarchical structures when DBSCAN processes data with uneven density distributions, this paper proposes a density-driven clustering framework, namely MSGB based on granular balls (GBs). This method uses the GB as the basic operational unit. First, it automatically determines the initial number of partitions using mean drift and initializes cluster centers based on local density peaks to avoid the sensitivity to initial values inherent in traditional -means. Second, it designs a radius calculation strategy based on the coefficient of variation-weighted median distance, allowing the GB scale to dynamically adjust according to local density variations, thereby preserving structural information while suppressing noise. Furthermore, by constructing a granular ball topological similarity graph, it transforms the density reachability determination into a search for connected components among granular balls, effectively handling scenarios with multi-density clusters and weak connections. To validate the effectiveness of the proposed method, this paper conducts comparative experiments on 10 synthetic datasets and 10 real-world datasets using ACC, NMI, and ARI as evaluation metrics. Specifically, on the synthetic datasets, MSGB improves ACC by 3.81%, NMI by 2.82%, and ARI by 4.49% compared to DBSCAN. On real-world datasets, it also achieves consistent improvements. The results show that MSGB outperforms several mainstream comparison algorithms on average across all datasets, demonstrating outstanding robustness and consistent advantages, particularly in noisy and non-uniform density scenarios, thereby validating the framework’s strong adaptability to data with complex density structures. The source code of the MSGB algorithm is available via the following network link https://github.com/Z-Lucky-M/MSGB .

Clustering on high-dimensional and low sample size (HDLSS) data remains a critical, persistent challenge where extreme sparsity and noise confound cluster analysis. This creates a dilemma: spectral methods fail as distance metrics degrade, while deep clustering tends to over-fit scarce data. To break this dilemma, a Self-Enhanced Density Clustering (SEDC) framework that integrates the cluster structure discovery and embedding representation learning into an iterative enhancement process is proposed in this paper. Specifically, SEDC uses adaptive density-derived centroids to parameterize probabilistic soft labels, which in turn supervise a lightweight multilayer perceptron (MLP) to learn the low-dimensional embedding from data. The resulting embedding provides a refined metric space for further generating superior labels in the subsequent interaction process. This feedback forms a mutual reinforcement that progressively enhances the discrimination of embedding while rigorously mitigating over-fitting. Extensive experiments on 43 challenging HDLSS datasets demonstrate state-of-the-art performance, substantially outperforming popular clustering methods. This work delivers a principled and promising solution for robust data clustering in HDLSS situations.

As a basic machine learning task, Multi-View Classification (MVC) has garnered considerable attention and achieved great success. However, the existing MVC methods, especially late fusion style ones still suffer from some problems: 1) hidden valuable information is not well exploited; 2) a lack of interaction before decision making. To address these problems, we propose a novel framework named ”TrashtoTreasure” that leverages mutual information to effectively exploit hidden valuable information. Specifically, the framework explicitly disentangles multi-view information into ”useful” components and ”trash” (noisy) components, and further extracts potentially valuable ”treasure” information from the ”trash”components of all views. Additionally, we design a tailored objective function that facilitates the effective separation of ”useful” and ”trash” components, as well as the synergistic extraction of ”treasure” information. This function guides model optimization through triple mutual information constraints. Experimental results on synthetic data and several real-world data sets verified the effectiveness and superiority of the proposed method. The fresh perspective offered by this article may inspire more interesting exploration in this direction. The codes are available athttps://github.com/jiezhang054/TrashToTreasure.

Multivariate time series classification (MTSC) requires a model capable of capturing both localized temporal patterns and long-range dependencies while effectively modeling complex inter-variable relationships. Existing convolutional neural network (CNN)-based capsule models suffer from limited receptive fields, constraining their ability to model long-range dependencies, while transformer-based capsule models rely solely on self-attention, which, despite its effectiveness in capturing global features, struggles with preserving local structures and efficiently processing long sequences. To overcome these limitations, we propose KACapMamba, a Knowledge-Aware State-Space Capsule Network, which integrates three attentive Mamba blocks with a routing layer to achieve hierarchical temporal modeling. Unlike conventional transformer-based methods that primarily depend on self-attention for global dependency modeling, each attentive Mamba block in KACapMamba fuses 1-dimensional CNNs, self-attention, state-space module (SSM), and mutual cross-attention, enabling a more structured and adaptive feature representation. Self-attention ensures effective long-range dependency modeling, while SSM provides a recurrent-state mechanism, inherently better suited for sequential processing compared to purely attention-based architectures, thereby enhancing temporal continuity and long-term pattern retention. Notably, mutual cross-attention addresses the limitations of traditional fusion strategies such as element-wise addition or multiplication, which lack the capacity to selectively enhance relevant features. By dynamically reweighting interactions between features, mutual cross-attention enables more expressive, context-aware representations, leading to improved feature disentanglement and inter-variable modeling. Additionally, the routing layer further enhances hierarchical feature disentanglement by refining capsule activations, reinforcing structural coherence and feature selectivity. Experiments conducted across the UEA benchmark archive demonstrate that KACapMamba consistently achieves the highest ‘win’/‘tie’/‘lose’/‘best’ ratios when evaluated against 10 leading transformer and Mamba architectures under both$Accuracy$and$F_{1}$metrics. Moreover, in comparison with 22 state-of-the-art MTSC models, it again secures the most favorable performance profile, demonstrating a clear and statistically supported advantage across both evaluation measures.

Outlier detection refers to the identification of anomalous samples that deviate significantly from the distribution of normal data and has been extensively studied and used in a variety of practical tasks. However, most unsupervised outlier detection methods are carefully designed to detect specified outliers, while real-world data may be entangled with different types of outliers. In this study, we propose a fuzzy rough sets-based multi-scale outlier detection method to identify various types of outliers. Specifically, a novel fuzzy rough sets-based method that integrates relative fuzzy granule density is first introduced to improve the capability of detecting local outliers. Then, a multi-scale view generation method based on granular-ball computing is proposed to collaboratively identify group outliers at different levels of granularity. Moreover, reliable outliers and inliers determined by the three-way decision are used to train a weighted support vector machine to further improve the performance of outlier detection. The proposed method innovatively transforms unsupervised outlier detection into a semi-supervised classification problem and for the first time explores the fuzzy rough sets-based outlier detection from the perspective of multi-scale granular balls, allowing for high adaptability to different types of outliers. Extensive experiments carried out on both artificial and UCI datasets demonstrate that the proposed outlier detection method significantly outperforms the state-of-the-art methods, improving the results by at least 8.48% in terms of the Area Under the ROC Curve (AUROC) index. The source codes are released at https://github.com/Xiaofeng-Tan/MGBOD

Graph neural networks (GNNs) are recognized as a significant methodology for handling graph-structure data. However, with the increasing prevalence of learning scenarios involving multiple graphs, traditional GNNs mostly overlook the relationships between nodes across different graphs, mainly due to their limitation of traditional message passing within each graph. In this paper, we propose a novel GNN architecture called cross-graph interaction networks (GInterNet) to enable inter-graph message passing. Specifically, we develop a cross-graph topology construction module to uncover and learn the potential topologies between nodes across different graphs. Furthermore, we establish inter-graph message passing based on the learned cross-graph topologies, achieving cross-graph interaction by aggregating information from different graphs. Finally, we employ cross-graph construction functions involving the relationships between contextual information and cross-graph topology structure to iteratively update the cross-graph topologies. Different to existing related approaches, GInterNet is designed as a cross-graph interaction paradigm for inter-graph message passing. It enables multi-graph interaction during the message passing process. Additionally, it is a plug-and-play framework that can be easily embedded into other models. We evaluate its performance in semi-supervised and unsupervised learning scenarios involving multiple graphs. A detailed theoretical analysis and extensive experiment results have shown that GInterNet improves the performance and robustness of the base models.

In multisource information fusion (MSIF), Dempster–Shafer evidence (DSE) theory offers a useful framework for reasoning under uncertainty. However, measuring the divergence between belief functions within this theory remains an unresolved challenge, particularly in managing conflicts in MSIF, which is crucial for enhancing decision-making level. In this paper, several divergence and distance functions are proposed to quantitatively measure discrimination between belief functions in DSE theory, including the reverse evidential KullbackLeibler (REKL) divergence, evidential Jeffrey’s (EJ) divergence, evidential JensenShannon (EJS) divergence, evidential$\chi ^{2}$(E$\chi ^{2}$) divergence, evidential symmetric$\chi ^{2}$(ES$\chi ^{2}$) divergence, evidential triangular (ET) discrimination, evidential Hellinger (EH) distance, and evidential total variation (ETV) distance. On this basis, a generalized$f$-divergence, also called the evidential$f$-divergence (Ef divergence), is proposed. Depending on different kernel functions, the Ef divergence degrades into several specific classes: EKL, REKL, EJ, EJS, E$\chi ^{2}$and ES$\chi ^{2}$divergences, ET discrimination, and EH and ETV distances. Notably, when basic belief assignments (BBAs) are transformed into probability distributions, these classes of Ef divergence revert to their classical counterparts in statistics and information theory. In addition, several Ef-MSIF algorithms are proposed for pattern classification based on the classes of Ef divergence. These Ef-MSIF algorithms are evaluated on real-world datasets to demonstrate their practical effectiveness in solving classification problems. In summary, this work represents the first attempt to extend classical$f$-divergence within the DSE framework, capitalizing on the distinct properties of BBA functions. Experimental results show that the proposed Ef-MSIF algorithms improve classification accuracy, with the best-performing Ef-MSIF algorithm achieving an overall performance difference approximately 1.22 times smaller than the suboptimal method and 14.12 times smaller than the worst-performing method.

Attribute reduction is widely employed to improve the efficiency and accuracy of data analysis by eliminating redundant and irrelevant attributes from datasets. However, with the emergence of growing big data , the sequential execution of such algorithms becomes time-consuming and requires distributed computing capabilities to achieve scalable parallelization . This study proposes a novel attribute reduction algorithm for neighborhood decision systems. We introduce two novel metrics—the neighborhood evidential conflict degree (NECD) and neighborhood evidential conflict rate (NECR)—to compute heterogeneity between samples in the neighborhood and assess the significance of attributes in the feature space , respectively. These metrics assess the quality and selection of attribute subsets in attribute reduction, improving classification accuracy and computational efficiency. We also develop a sequentially forward selection attribute reduction method to select a feature subset through the defined NECR. Finally, we develop a distributed attribute reduction algorithm implemented in Apache Spark . Our approach involves a two-phase Map-Reduce process for K -Nearest Neighbors search, evidence combination, and NECR computation . NECR, as a measure of feature subset quality, enhances the feature subset's decision approximation capability of the data. Experimental results on small and large datasets demonstrate that the proposed algorithm outperforms benchmarking algorithms regarding classification accuracy and computational efficiency.

Dynamic link prediction aims to predict future connections among unconnected nodes in a network. It can be applied for friend recommendations, link completion, and other tasks. Network representation learning algorithms have demonstrated considerable effectiveness in various prediction tasks. However, most network representation learning algorithms are based on homogeneous networks and static networks for link prediction that do not consider rich semantic and dynamic information. Additionally, existing dynamic network representation learning methods neglect the neighborhood interaction structure of the node. In this work, we design a neighbor-enhanced dynamic heterogeneous attributed network embedding method (NeiDyHNE) for link prediction. In light of the impressive achievements of the heuristic methods, we learn the information of common neighbors and neighbors’ interaction in heterogeneous networks to preserve the neighbors proximity and common neighbors proximity. NeiDyHNE encodes the attributes and neighborhood structure of nodes as well as the evolutionary features of the dynamic network. More specifically, NeiDyHNE consists of the hierarchical structure attention module and the convolutional temporal attention module. The hierarchical structure attention module captures the rich features and semantic structure of nodes. The convolutional temporal attention module captures the evolutionary features of the network over time in dynamic heterogeneous networks. We evaluate our method and various baseline methods on the dynamic link prediction task. Experimental results demonstrate that our method is superior to baseline methods in terms of accuracy.

Transformer interpretability research is a hot topic in the area of deep learning. Traditional interpretation methods mostly use the final layer output of the Transformer encoder as masks to generate an explanation map. However, These approaches overlook two crucial aspects. At the coarse-grained level, the mask may contain uncertain information, including unreliable and incomplete object location data; at the fine-grained level, there is information loss on the mask, resulting in spatial noise and detail loss. To address these issues, in this paper, we propose a two-stage coarse-to-fine strategy (C2F-Explainer) for improving Transformer interpretability. Specifically, we first design a sequential three-way mask (S3WM) module to handle the problem of uncertain information at the coarse-grained level. This module uses sequential three-way decisions to process the mask, preventing uncertain information on the mask from impacting the interpretation results, thus obtaining coarse-grained interpretation results with accurate position. Second, to further reduce the impact of information loss at the fine-grained level, we devised an attention fusion (AF) module inspired by the fact that self-attention can capture global semantic information, AF aggregates the attention matrix to generate a cross-layer relation matrix, which is then used to optimize detailed information on the interpretation results and produce fine-grained interpretation results with clear and complete edges. Experimental results show that the proposed C2F-Explainer has good interpretation results on both natural and medical image datasets, and the mIoU is improved by 2.08% on the PASCAL VOC 2012 dataset.

Partial label learning (PLL) tackles scenarios where the unique ground-truth label of each sample is concealed within a candidate label set. Dimensionality reduction, considering labeling confidence estimation, has become a promising strategy to enhance the generalization performance of PLL models. However, current studies achieve dimensionality reduction, often relying on kNN-based labeling confidence estimation or disregarding potential labeling information. To address this issue, this paper proposes a novel Confidence-induced granular Partial label feature selection method using Dependency and Similarity (CPDS), which consists of two phases: Labeling Confidence Estimation (LCE) and Feature Selection (FS). For LCE, through granular ball computing, the feature space's similarity and the label space's correlation between the training data and the granular ball can be fused simultaneously, thereby effectively reconstructing more credible labeling confidence from candidate labels with more diverse semantic representation information. In the FS stage, by leveraging the LC with more diverse information, the proposed PLL neighborhood decision system further effectively combines feature dependency and label similarity to identify a feature subset with more discriminative capabilities, thereby achieving better performance for classification tasks. Among them, feature dependency effectively utilizes the dependency between neighborhoods and equivalence relations, while label similarity fully exploits the similarity between each sample and its neighbors. Extensive experiments show that CPDS significantly outperforms the compared approaches in most cases on nine controlled UCI datasets and five real-world datasets, demonstrating the superiority of the proposed method.

Knowledge discovery of heterogeneous data is an active topic in knowledge engineering. Feature selection for heterogeneous data is an important part of effective data analysis. Although there have been many attempts to study the feature selection for heterogeneous data, there are still some challenges, such as the unbalanced problem between the stability and validity of the designed model. Hence, this paper focuses on how to design an effective and robust heterogeneous feature selection method, namely a zentropy-based uncertainty measure for heterogeneous feature selection(Ze-HFS). Different from other entropy-based uncertainty measures, the proposed method does not consider single-level information measures but systematically analyzes and integrates the information between different granular levels, which has an obvious advantage in the study of heterogeneous data knowledge discovery. Specifically, a heterogeneous distance metric is first introduced to construct heterogeneous neighborhood granules and heterogeneous neighborhood rough sets(HNRS). Then, the zentropy-based uncertainty measure is developed by analyzing the granular level structure in the HNRS model. Finally, two significant measures based on the above research are designed for heterogeneous feature selection. Compared with other state-of-the-art methods, the experimental results on 18 public datasets demonstrate the robustness and effectiveness of the proposed method.

This paper proposes an assessor-guided learning strategy for continual learning where an assessor guides the learning process of a base learner by controlling the direction and pace of the learning process thus allowing an efficient learning of new environments while protecting against the catastrophic interference problem. The assessor is trained in a meta-learning manner with a meta-objective to boost the learning process of the base learner. It performs a soft-weighting mechanism of every sample accepting positive samples while rejecting negative samples. The training objective of a base learner is to minimize a meta-weighted combination of the cross entropy loss function, the dark experience replay (DER) loss function and the knowledge distillation loss function whose interactions are controlled in such a way to attain an improved performance. A compensated over-sampling (COS) strategy is developed to overcome the class imbalanced problem of the episodic memory due to limited memory budgets. Our approach, Assessor-Guided Learning Approach (AGLA), has been evaluated in the class-incremental and task-incremental learning problems. AGLA achieves improved performances compared to its competitors while the theoretical analysis of the COS strategy is offered. Source codes of AGLA, baseline algorithms and experimental logs are shared publicly in https://github.com/anwarmaxsum/AGLA for further study.

In recent years, it has been difficult for multilabel classification to obtain complete multilabel data in real-world applications, and even a large number of labels for training samples are randomly missed. As a result, the classification task of incomplete multilabel data with missing labels faces formidable challenges. This paper presents a two-stage-neighborhood-based multilabel classification method for incomplete data with missing labels in neighborhood decision systems. First, to solve the problem of selecting the neighborhood radius manually, as well as balancing the samples in the neighborhood, the neighborhood radius based on the feature distribution function is defined, and the differences and similarities between samples through the identifiable and indiscernible matrices are, respectively, computed. Then, a restoration method for missing feature values is proposed for use in the first stage. Second, to consider the nonlinear relationship among features, a neighborhood-based fuzzy similarity relationship between samples is investigated based on the Gaussian kernel function. By integrating the fuzzy similarity relationship matrix, label-specific feature matrix, and label correlation matrix, an objective function based on the regression model is presented, the optimal solutions to the label-specific feature and label correlation matrices based on the gradient descent strategy are provided, and a new multilabel classification method with missing labels is developed during the second stage. Finally, two-stage multilabel classification algorithms are designed. Experiments on 18 multilabel data sets demonstrate that our designed algorithms are effective not only for recovering missing feature values, but also for improving the classification performance of data with missing labels.

As an important technique for dealing with transactional database in the field of data mining, high-utility itemset mining (HUIM) can be used to discover itemsets which have a high utility. However, it has a bias when towarding the item combinations which have more exhibition period since they have more opportunity to generate a high utility. To address this, the on-shelf time period of items need to be considered, thus on-shelf utility mining (OSUM) can be applied in the application which is more closer to the actual situation. Currently several models have been proposed to deal with the OSUM problem, but they still suffer from the requirement that it needs to maintain a massive candidates in memory and to scan database many times. In this paper, we propose an effective algorithm named OSUMI (On-Shelf Utility Mining from Itemset-based data) which can discover the on-shelf itemsets with high utility in a more practical way. More precisely, in order to avoid the problems of high memory consumption, OSUMI applies some properties of on-shelf utility. Besides, two upper-bounds named subtree utility and local utility are applied to prune the search space. Finally, an extensive experimental study on two real on-shelf datasets shows that our proposed algorithm can be significantly faster than the state-of-the-art algorithm for this mining task.

Autonomous construction of deep neural network (DNNs) is desired for data streams because it potentially offers two advantages: proper model's capacity and quick reaction to drift and shift. While self-organizing mechanism of DNNs remains an open issue, this task is even more challenging to be developed for standard multi-layer DNNs than that using the different-depth structures, because addition of a new layer results in information loss of previously trained knowledge. A Neural Network with Dynamically Evolved Capacity (NADINE) is proposed in this paper. NADINE features a fully open structure where its network structure, depth and width, can be automatically evolved from scratch in the online manner and without the use of problem-specific thresholds. NADINE is structured under a standard MLP architecture and the catastrophic forgetting issue during the hidden layer addition phase is resolved using the proposal of soft-forgetting and adaptive memory methods. The advantage of NADINE, namely elastic structure and online learning trait, is numerically validated using nine data stream classification and regression problems where it demonstrates performance's improvement over prominent algorithms in all problems. In addition, it is capable of dealing with data stream regression and classification problems equally well.

Due to the fact that conventional evolution-based attribute reduction algorithms are poor efficiency in accomplishing large-scale attribute reduction, a novel and efficient quantum cooperative co-evolutionary algorithm (named QCCAR) for minimum attribute reduction optimization in large-scale datasets is proposed in this paper. First, the self-adaptive quantum rotation angle and quantum entanglement strategies are adopted to update the operation of quantum revolving door, and the population diversity and convergence to the global optimum ensure to be improved fast. Second, a local-global best performance based cooperative co-evolutionary paradigm is designed to divide large-scale attribute sets into reasonable subsets, which are adaptively produced based on the assignment of decomposer credit and probability. Third, the representative of the subpopulation is selected to evolve the corresponding decomposed attribute subset so that the global optimization reduction set can be obtained quickly. The experimental results demonstrate that the proposed algorithm has better feasibility and effectiveness, comparison with other state-of-the-art algorithms. So it can provide an efficient solution to finding minimum attribute reduction for large-scale datasets.