Feature Selection (FS) is essential for high-dimensional data analysis. It results in compact and information-preserving representations that offer superior discriminability, improved computational efficiency, and greater interpretability. However, existing methods struggle to model complex inter-feature couplings. Reinforcement Learning (RL)-based FS approaches also face large action spaces, ambiguous credit assignment, and redundant agent behaviors. To address these issues, we propose Elastic Agents for Cooperative Feature Selection (EAC-FS), a scalable and interpretable Multi-Agent Reinforcement Learning (MARL) framework. EAC-FS treats FS as a dynamic cooperative process. Firstly, it introduces elastic agents that adaptively transfer feature ownership to reduce redundant computation and promote specialization. Furthermore, a local observation encoder captures structural information within each feature group, while a hierarchical credit assignment scheme separates global objectives from local contributions. A parallel transfer policy further coordinates feature routing across agents. Ultimately, EAC-FS is the first unified MARL formulation in which feature grouping, transfer, and selection evolve jointly within a single sequential decision process. Extensive experiments on nine benchmark datasets show that EAC-FS outperforms both classical and RL-based methods in accuracy, robustness, and cross-classifier generalization.

Achieving collective consensus in large-scale group decision-making (LSGDM) is increasingly challenging due to the explosion of heterogeneous information sources. The core problem lies in distilling coherent outcomes from massive datasets characterized by sparse user ratings, uncertain social trust, and complex strategic interactions. Existing approaches often fragment this problem, treating trust modeling, data completion, and consensus negotiation as isolated processes, thereby failing to capture their intrinsic interdependence. To address this unified challenge, we propose a granular ball (GB) evolutionary game-based framework. Unlike traditional point-based models, we represent each decision maker as a center–radius GB, where the radius inherently encodes uncertainty and social reliability. We introduce an adaptive community detection strategy based on GB distances to reveal latent groups with high consensus potential without requiring prior structural knowledge. Furthermore, we design a two-stage dynamic consensus mechanism that combines payoff-driven intra-group opinion evolution with inter-group coordination. During consensus reaching, individual strategies, opinions, and trust weights interact dynamically, while the previously obtained community structure provides hierarchical guidance for the evolution process. Experimental results demonstrate that the proposed method achieves robust and scalable consensus formation under sparse and uncertain conditions, outperforming existing approaches in adaptability and solution quality. The source code is openly available at https://github.com/JustinaZhan/GBLSGDM.

Multiple kernel clustering (MKC) addresses multi-view clustering by detecting nonlinear structures within base kernel spaces to reveal shared manifold similarities. However, traditional methods limit solutions to predefined kernel spaces and hinder gradient propagation due to discrete eigenvalue updates. To overcome these limitations, we propose Neural Connected Kernel-based Multiple Kernel Clustering (NCKMKC), which builds neural networks to generate adaptive connected kernels, enabling differentiable eigenvalue optimization by relaxing orthogonality constraints and broadening the solution space. Additionally, a novel density-based Local Connectivity Peak (LCP) model reinforces the block-diagonal structure, balancing local structure with global similarity preservation under rank constraints. An efficient iterative algorithm is designed to resolve the optimization. Extensive empirical experiments confirm the significant performance advantages over all leading state-of-the-art alternatives.

To address the challenge of rejecting cross-manifold interference in non-linear data clustering, this paper proposes a novel method termed Local Hyperplane-Constrained Self-Representation for Manifold Clustering. By incorporating a local hyperplane constraint within each sample’s neighbors from other manifolds, the framework explicitly models local geometric separability to ensure that each sample is reconstructed primarily from points on the same manifold while suppressing neighbors from other manifolds. Theoretical analysis establishes error bounds for the model and provides a sufficient condition for manifold preservation, enhancing the method’s interpretability. Extensive evaluation on 12 synthetic and 10 real-world datasets demonstrate that the proposed approach significantly outperforms eleven state-of-the-art algorithms. Specifically, the method yields an average accuracy improvement of approximately 8%-15% over representative baseline methods, with gains exceeding 20% on certain datasets. Furthermore, the model achieves 100% clustering accuracy on the PIE dataset and demonstrates high computational efficiency by converging within just five iterations. The source code is available at https://github.com/HNU-MingjieCai/LHCMC.

Missing Value Imputation (MVI) is a critical challenge in data science and machine learning, particularly in high-dimensional tabular data. Existing methods exhibit limitations in capturing complex relationships between variables, especially in effectively utilizing latent causal structures. This study proposes a causal discovery and attentionbased MVI method (Causal Attention-based Missing value Imputation, CAMI), which introduces causal discovery techniques to generate causal graphs that guide attention allocation. By combining multi-head self-attention, it dynamically captures the relationships between variables, thereby improving imputation performance. Experimental results show that CAMI outperforms traditional and deep learning-based imputation methods across multiple real-world datasets and varying missing ratios, demonstrating stability and robustness, especially in data with high missing proportions. This method not merely increases imputation accuracy but also enhances data relationship interpretability, offering new insights for MVI tasks in tabular datasets.

Although density peaks clustering (DPC) is an efficient clustering algorithm, it performs poorly on manifold data, density-imbalanced data, and cluster boundary overlapping data. Moreover, DPC is highly sensitive to the cutoff distance. To address these issues, a novel density peak clustering algorithm via fusing natural neighbor and fuzzy information (FNaN-DPC) is proposed. Firstly, the adaptive local density metric based on natural neighbor is introduced to eliminate the high density differences among different clusters to accurately recognize cluster centers. Secondly, a label propagation method based on natural neighbor is proposed to adapt to manifold data. Thirdly, the termination condition for label propagation is set to distinguish the core and boundary regions of clusters. Finally, the designed fuzzy membership function is utilized to determine the attribution of data points in the boundary region, which enables the FNaN-DPC algorithm to effectively process data with overlapping cluster boundaries. The experimental results on both synthetic and real-world datasets show the effectiveness and superiority of FNaN-DPC.

Graph convolutional neural networks (GCNs) have demonstrated effectiveness in processing graph structure. Due to the diversity and complexity of real-world graph data, heterogeneous GCN have attracted significant attention. However, existing research predominantly relies on explicit connections to explore graph heterogeneity. In the case of edgeless graphs, such as information systems, the absence of direct edges poses a significant challenge for employing GCNs to analyze the latent heterogeneity within these graphs. Traditional approaches overlook the topological features of information systems, resulting in information loss. This article introduces a heterogeneous graph convolutional neural network based on shadowed deviation relationship (SDHGCN) to investigate the heterogeneity of information systems, thereby improving the generalizability of heterogeneous GCNs. First, shadow deviation relationship and attribute deviation relationship are constructed derived from shadow sets and information gain, respectively. Then, dexterously integrated with the feature matrix of the information system (the relationship between objects and attributes), a highly expressive heterogeneous graph is constructed. Second, by performing graph convolution operations on the heterogeneous graph, effective node representations can be obtained to complete node classification tasks. Finally, the effectiveness and nonrandomness of SDHGCN are validated by extensive comparison and ablation experiments.

Clustering by fast search and find of density peaks (DPC), a classic density-based algorithm, excels in identifying clusters of arbitrary shape. However, it struggles in recognizing complex structures due to challenges in selecting density peaks and allocating non-central points. To address these issues, we propose an anchor graph based connectivity peaks clustering method which is the connection between anchor graph and density-based clustering, called AG-CPC. Firstly, it introduces a new concept of connectivity by analyzing the divergence and discreteness of neighborhood adjacency graph to detectlow-density clusters and border points. Secondly, a robust two-stage assignment strategy using an adaptive parent-child relationships based on data distribution characteristics, is proposed to reduce the wrong allocation of non-central points. Lastly, a local method for constructing anchor graphs is introduced, combined with fuzzy connectivity and boundary domains of clusters, to scale down the anchor graphs and establish the connection among anchor points. The experiments demonstrate the efficiency and stability of the proposed algorithm compared to state-of-the-art algorithms on synthetic, real-world, and image datasets.

In real-world tasks, multiple agents often need to coordinate with one another due to their individual private observations and restricted communication abilities. A representative research direction is the deep multi-agent reinforcement learning value decomposition, which decomposes the global shared joint action value function Qtot(i, u) into their respective action value functions Qi(ai, ui) to guide the behavior of individuals. They all follow the IGM (Individual-Global-Max) principle, obeying the addable assumption and the monotonic assumption to support effective local decision making. However, to achieve scalability, existing MARL algorithms often compromise either the expressive power of their value function representations or the consistency of the IGM principles. This compromise can potentially result in instability or poor performance when dealing with complex tasks. In this paper, we introduce a novel algorithm called MDF-a Multi-Dueling Framework for Multi-Agent Reinforcement Learning. We innovatively propose the V-IGM constraint principle and correct the incomplete expression of the constant term c(i) of the Qatten algorithm to further refine the decomposition of the joint action value function Qtot(i, u). The MDF algorithm innovatively utilizes the Dueling Network architecture for decomposing the joint action value function Qtot(i, u). Additionally, it incorporates the multi-attention mechanism to achieve an even more refined decomposition of Qtot(i, u). Experiments show that MDF algorithm outperforms the most advanced MARL algorithm in StarCraftl7 maps (e.g. 3 m, 8 m, 2m-vs-1z, 2m-vs-1sc, 2s3z, 3s-vs-4z, 3s-vs-5z, 3s5z, 1c3s5z, bane-vs-bane).

In the era of big data, large scale group decision-making (LSGDM) with social networks (SNs) (namely, SN-LSGDM) has become a hot topic in the field of decision science. Faced with the explosive growth of information, decision-makers (DMs) face immense challenges in processing and integrating vast amounts of data, often finding it difficult to fully comprehend all the information, leading to potentially incomplete expressions of their fuzzy preference relations (FPRs). This limitation in information processing not only affects the quality of decision-making but also increases the difficulty and cost of reaching a consensus. To overcome these challenges and enhance the efficiency and accuracy of decision-making, this paper designs a consensus model that minimizes adjustment costs in light of a dynamic trust network. Firstly, we introduce a measurement method based on K-nearest neighbor (KNN) information, which comprehensively considers the trust level of DMs and the similarity of preference relations, effectively filling in missing preference information and improving the completeness and accuracy of decision-making. In addition, an improved k-means clustering algorithm is adopted, which takes into account the mutual influences between DMs and the cost of unit adjustment. On this basis, a two-stage minimum adjustment cost consensus reaching mechanism based on three-way decision (TWD) is proposed, using comprehensive adjustment priority as the criterion for division, to achieve feedback adjustment at the individual and subgroup levels, ensuring the coordination and consistency of the decision-making plan. At the same time, an optimization model is introduced to achieve cost minimization. Through detailed case studies and comparative analysis, the feasibility and superiority of this method in practical applications have been demonstrated.

In multi-label learning, feature selection plays a key role. This paper delves into the study label relationships within the field of multi-label feature selection, with a particular focus on local label relationships. Most existing research explores these local relationships through clustering and other methods. These approaches may overlook the fact that the local correlations between labels may only manifest in specific subsets of the data, and there may be more complex semantic relationships between labels. Additionally, traditional logical label representation methods may not fully capture the connections between the sample space and the label space, whereas converting logical labels into label distributions with relative importance can provide more effective supervision information. At the same time, existing multi-label feature selection methods based on fuzzy rough sets are deficient in handling the interrelationships between labels and sensitive to noise. Motivated by these challenges, this paper proposes a new multi-label feature selection algorithm that combines label enhancement and fuzzy rough sets. First, we propose method to identify neighborhood granules with high-level semantic relationships to explore local structure of the data, and based on this, we propose a novel label enhancement algorithm. Secondly, we transform the decision classes in traditional fuzzy rough set model into fuzzy decision classes, and propose an innovative multi-label fuzzy decision system based on label distribution. Finally, we design a new type of multi-label feature selection method based on high-level semantic relationships (HSR-MLFS). In the experiments, compared with other seven algorithms on eleven real-world datasets, the results show the superiority of the proposed algorithm.

Feature selection can select important features to address dimensional curses. Subspace learning, a widely used dimensionality reduction method, can project the original data into a low-dimensional space. However, the low-dimensional representation is often transformed back into the original space, resulting in information loss. In addition, gate function-based methods in Takagi-Sugeno-Kang fuzzy system (TSK-FS) are commonly less discrimination. To address these issues, this article proposes a novel feature selection method that integrates subspace learning with TSK-FS. Specifically, a projection matrix is used to fit the intrinsic low-dimensional representation. Subsequently, the low-dimensional representation is fed to TSK-FS to measure its availability. The firing strength is slacked so that TSK-FS is not limited by numerical underflow. Finally, the l( 2,1)-norm is introduced to select significant features and the connection to related works is discussed. The proposed method is evaluated against six state-of-the-art methods on 17 datasets, and the results demonstrate the superiority of the proposed method.

In the era of Big Data, the integration and fusion of heterogeneous information have become essential for addressing complex decision-making challenges in large-scale group decision-making (LSGDM), where expanding scale and diverse participant behaviors increasingly demand advanced techniques to enhance efficiency, fairness, and accuracy. To meet these demands, this article proposes a novel framework that leverages information-fusion principles to optimize group decision-making processes. First, an enhanced fuzzy C-means algorithm, termed Trust-based regularized fuzzy C-means, is introduced. By incorporating a regularization term derived from trust relationships, it improves clustering precision and enables finer segmentation of decision-makers (DMs), thus laying solid groundwork for consensus. Building on this, we develop an optimization model integrating three-way decision theory to resolve asynchronous differences among experts. The model uses dynamic trust updates to guide DMs from the negative region toward those in the positive region, with special emphasis on rapid consensus in emergencies. Furthermore, the study, for the first time, systematically investigates manipulative and herd behaviors within large datasets; adopting a cautious strategy to mitigate their impact on fairness and effectiveness, it embeds pseudotrust identification into the framework to further refine the decision environment. Extensive case studies and comparative experiments demonstrate that the proposed method significantly improves decision-making efficiency, fairness, and accuracy, offering new perspectives and practical tools for managing complex information and optimizing group behaviors in LSGDM.

Motivated by the potential application of formal concept analysis in supporting learning, we attempt to take advantage of the relations between objects to assist in the problem recommendation. This paper is to provide a preliminary preparation for the establishment of a mathematical model and to focus on the theoretical aspects. To achieve this, first, we propose ℂ_i -connected relations between objects and introduce the concepts of ℂ_i -connected context. Next, we investigate the closedness of ℂ_i -connectedness regarding some mapping images, subcontexts and products. Finally, we explore the relationship between some special complete lattices and ℂ_i -connected contexts. It is proved that the concept lattices generated by ℂ_i -connected contexts can be represented by some atomistic complete lattices.

Outlier detection is a crucial task for ensuring the reliability of data analysis, aiming at identifying objects that markedly differ from typical patterns in the dataset. Recently, many methods based on fuzzy rough sets have shown promising performance. However, these methods overlook the influence of redundant attributes and include the relationships between outliers in the analysis. Targeting these important problems, we propose a novel approach called Prototype-based Fuzzy Rough Sets (PFRS), which performs outlier detection via prototype learning based on the selection of separable attributes. Specifically, information entropy is applied to select significant attributes, enhancing the separability of the feature space. More importantly, by employing prototype learning to acquire representative objects, PFRS effectively eliminates the impact of relationships among outliers. In addition, the fuzzy similarity between prototypes and objects is evaluated to reconstruct the traditional fuzzy upper and lower approximations. Finally, more reliable outlier scores are derived from PFRS. Extensive experiments using widely adopted algorithms verify the effectiveness of PFRS, confirming its outstanding performance.

Multi-label feature selection can select representative features to reduce the dimension of data. Since existing multi-label feature selection methods usually suppose that the significance of all labels is consistent, the relationships between samples in the entire label space are generated straightforwardly such that the shape of label distribution and the property of class-imbalance are ignored. To address these issues, we propose a novel multi-label feature selection approach. Based on non-negative matrix factorization (NMF), the similarities between the logical label and label distribution are constrained, which ensures that the shape of label distribution does not deviate from the underlying actual shape to some extent. Further, the relationships between samples in label space and feature space are restricted by graph embedding. Finally, we leverage the properties of label distribution and class-imbalance to generate the relationships between samples in label space and propose a multi-label feature selection approach based on fuzzy information entropy. Eight state-of-the-art methods are compared with the proposed method to validate the effectiveness of our method.

As an important part of machine learning, clustering methods have been continuously paid attention to. Current clustering methods divide data objects usually based on Euclidean metric, which is a basic and effective metric method. However, with the high dimensionality of data and the diversification of data representation, the complexity of the spatial structure of real-world data continues to rise. Classical clustering methods face many challenges such as insufficient clustering effectiveness, the sensitivity of clustering method parameters, and lack of stability of clustering results. Aiming at the above problems, this paper designs a non-Euclidean metric and constructs a multi-granularity staged clustering method based on the metric. First of all, this paper uses the sequential relationship of each feature of the data to construct a similarity measure between objects from the perspective of positive and negative granularity to improve the clustering algorithm’s understanding of complex spatial structure data. Secondly, this paper designs the attenuation-diffusion pattern divides and conquers according to the distribution characteristics of data objects in different patterns, and uses the heuristic idea to effectively cluster the data in stages from local to global. Again, based on the above, this paper proposes a clustering method based on multi-positive-negative granularity and attenuation-diffusion pattern, which can effectively deal with the challenges brought by complex spatial structure data to clustering methods. Finally, the effectiveness and robustness of the proposed method and advanced clustering methods are compared and analyzed on UCI real data sets. Experimental results show that the method proposed in this paper has obvious advantages in clustering results on complex spatial structure data. In addition, in the two directions of non-Euclidean metrics and multi-granularity clustering, the method proposed in this paper provides a new perspective for effectively dealing with the design of clustering methods on complex spatial structure data.

Three-way decision (3WD) is a powerful tool for granular computing to deal with uncertain data, commonly used in information systems, decision-making, and medical care. Three-way decision gets much research in traditional rough set models. However, three-way decision is rarely combined with the currently popular field of machine learning to expand its research. In this paper, three-way decision is connected with SVM, a standard binary classification model in machine learning, for solving imbalanced classification problems that SVM needs to improve. A new three-way fuzzy membership function and a new fuzzy twin support vector machine with three-way membership (TWFTSVM) are proposed. The new three-way fuzzy membership function is defined to increase the certainty of uncertain data in both input space and feature space, which assigns higher fuzzy membership to minority samples compared with majority samples. To evaluate the effectiveness of the proposed model, comparative experiments are designed for forty-seven different datasets with varying imbalance ratios. In addition, datasets with different imbalance ratios are derived from the same dataset to further assess the proposed model’s performance. The results show that the proposed model significantly outperforms other traditional SVM-based methods.