The graph-based clustering aims to utilize structural information from graphs to provide clustering solutions. However, many existing graph clustering methods separate graph construction from the learning of clustering results, and rely on the assumption of consistent feature importance, which often leads to suboptimal clustering outcomes. Anchor-based graph clustering offers an efficient and scalable solution for clustering tasks. Nevertheless, the need to manually specify the number of anchors limits its practicality. Motivated by these issues, this paper proposes a method called Multi-granularity Granular-ball Anchor Graph Clustering with self-weighting (MGAGC). The MGAGC utilizes granular-ball computing to adaptively generate granular-ball anchors based on the data distribution, where the number of granular-ball anchors is much smaller than the number of data samples. Then, by enabling interaction between fine-granularity sample points and coarse-granularity granular-ball anchors in a self-weighting feature space, the MGAGC integrates graph construction with the learning of clustering results. Extensive experiments are conducted on fourteen public datasets to compare the proposed MGAGC with nine classic or state-of-the-art baseline clustering methods. Experimental results show that MGAGC achieves an average ACC of 75.50% and an average NMI of 51.22%, outperforming other clustering methods by an average of 13.60% and 12.21%, respectively. Moreover, statistical test results indicate that its performance differences are statistically significant compared to most of the competing methods. Code is available at https://github.com/awaw-Liyely/2026-IPM-MGAGC . • Adaptive granular-ball anchors auto-counted for full data coverage. • Self-weighted features enable fine-coarse interaction for accurate similarity. • Unified graph-clustering via Laplacian rank gives direct cluster labels. • Experimental results show that the proposed model and algorithm perform well.

Outlier detection is an effective technique for identifying abnormal samples in complex data. Random walks effectively detect outliers by analyzing graph transition patterns. However, existing methods only consider local transitions and fail to capture complex structural patterns in complex data. Granular-ball computing based outlier detection methods have better robustness and efficiency. Nevertheless, these methods use a coarse-granularity representation of granular-balls and ignore the large number of sample information within the granular-balls. To address the above issues, this paper develops a bi-level granular-ball based second-order biased random walk outlier detection method. First, a bi-level granular-ball knowledge representation method is proposed to address the information distortion inherent in granular-ball computing-based methods. Then, a granular-ball anomaly membership evaluation metric is introduced, which leverages second-order biased random walk, to endow granular-balls with coarse-granularity anomaly degrees. Subsequently, a bi-level granular-ball anomaly classifier is designed to map coarse-granularity granular-ball anomaly degrees to fine-granularity sample-level anomaly degrees. Finally, a distilled outlier factor is defined, which selects optimal attribute sequences through granular-ball construction on attributes, for outlier detection. At the same time, a corresponding outlier detection algorithm is proposed. Experiments on datasets are conducted to compare the proposed algorithm with six other algorithms. The experimental results show that the algorithm has better performance and a certain degree of robustness.

Representation learning serves as a critical bridge between human cognition and the data world, constituting an essential component of machine learning architectures where comprehensiveness and flexibility are paramount. However, existing multi-view feature selection methods are constrained by the raw-scale representations, neglecting comprehensive depth-breadth integration and flexible adaptability. This paper presents multi-scale fuzzy fusion-based heterogeneous granular-ball flexible representation learning for multi-view feature selection (MFHGBFR). A comprehensive multi-view, multi-scale analytical foundation is established to promote depth-breadth representation learning, where views represent breadth and scales represent depth in human cognition. Heterogeneous granular ball-based flexible representations are adaptively developed via multi-scale fuzzy fusion, effectively capturing intricate data manifolds and implicit fuzzy patterns across multi-granularity spaces. Intricate data manifolds are fitted with heterogeneous rather than conventional homogeneous structures to improve the adaptability of representations' multi-granularity. Implicit fuzzy patterns are extracted with fuzzy approximation operators to mitigate fuzziness and uncertainty in a multi-granularity space. For the first time, granular-ball representation learning and feature selection are adaptively optimized in a unified one-step framework, rather than the conventional two-step frameworks, for flexible adaptability. An effective optimization algorithm with proven convergence is derived. Through the learned high-quality representations, the MFHGBFR manifests superior performance, robustness, and efficiency. Comparative experiments against contemporary state-of-the-art algorithms substantiate these advantages quantitatively and qualitatively.

Unsupervised feature selection aims to enhance the quality of unlabeled data, thereby improving the performance of subsequent unsupervised learning models. However, most of the existing unsupervised feature selection methods rely on single-granularity modeling, which reduces the expressive capability of data to some extent. In addition, the existing studies are generally based on a forward greedy feature selection strategy, which tends to fall into a local optimum. To address these issues, this paper proposes a novel unsupervised feature selection method for handling hybrid data, called unsupervised feature selection method using fuzzy graph momentum random walk in bi-level granular-ball knowledge space. Specifically, a Bi-level Granular-ball Knowledge Space (BGKS) is first constructed by combining fine granularity and coarse granularity representations through a hybrid Gaussian kernel function. Then, a multi-granularity fuzzy graph is built on the BGKS using upper and lower fuzzy approximation operators. Based on this graph, a Momentum Random Walk (MRW) mechanism is introduced to design the Fuzzy Graph Momentum Random Walk (FGMRW) model. Finally, an iterative unsupervised feature selection algorithm is developed. Extensive experiments on 20 public datasets demonstrate that, compared with existing algorithms, the proposed method is able to maintain or even improve clustering performance while selecting fewer features, thus achieving superior overall performance. The source code of this work is publicly available athttps://github.com/HongtaoGao-code/FGMRW-UFS.

Multiview data possess different discriminability in different views, which is challenging to catch but crucial for a feature selection model. Multiscale information, which represents vertical exploration in each view, is vital for further mining traits implied in multiview data. However, most existing studies neglect these beneficial multi-granulation characteristics. This study first embeds the multiscale information into the sparse learning framework for multiview feature selection. A class-specific discriminability and multiscale information-based multiview feature selection (CDMIMFS) method is proposed. It explores the fuzzy and uncertain class-specific discriminability which is inherently discrepant in different views by the fuzzy rough set theory. It relaxes the over strict requirement for complete consistency in multiscale information systems to make a trade-off, which further enhances discriminative feature selection. An effective iteration algorithm is proposed to solve the optimization. Both the theoretical proof and experimental demonstration of convergence are provided. Comprehensive experiments are conducted on the CDMIMFS compared with state-of-the-art algorithms. Results on different evaluation metrics exhibit the advantages of the proposed method.

Robust knowledge acquisition approaches are one of the research hotspots in data mining. The fuzzy dominance rough sets (FDRS) model is an important knowledge acquisition tool for ordinal classification tasks. However, it has been proved in practice that this model usually performs poorly fault tolerance, and only one noisy sample can cause huge interference in acquiring knowledge. Attribute reduction is one of the nontrivial applications of the FDRS. At present, most attribute reduction methods for ordinal classification tasks mainly focus on the dependence of decision to attributes, while ignoring the information provided by the separability of classes and the correlation of attributes for ordinal classification. In view of these two issues, this article first proposes a robust FDRS model with filterable noise samples. Then, the class-separability and attribute-correlation are explored in robust fuzzy dominance rough approximation space, and corresponding attribute evaluation index is designed. Finally, an attribute reduction algorithm is designed to select the attribute subset with the highest classification performance. The experimental results show that the proposed algorithm has better robustness and classification performance.

Feature selection methods with antinoise performance are effective dimensionality reduction methods for classification tasks with noise. However, there are few studies on robust feature selection methods for monotonic classification tasks. The fuzzy dominance rough set (FDRS) model is a nontrivial knowledge acquisition tool, which is widely used in feature selection of monotonic classification tasks. Nonetheless, this model has been proved in practice to be generally poorly fault-tolerance, and only one noisy sample can cause huge interference in acquiring knowledge. In view of these two issues, this article first designs an adaptive$K$-nearest neighbors strategy to calculate the density of samples. The noisy samples are identified according to their densities, and then an active antinoise FDRS model is proposed. Then, in the active antinoise fuzzy dominance rough approximation space, the class-separability is evaluated by the approximation operators of the proposed model, and the feature-redundancy is evaluated by the fuzzy ranking conditional mutual information. On this basis, a feature evaluation index is designed comprehensively considering class-separability and feature-redundancy. Finally, a feature selection algorithm is designed to select the feature subset with the highest classification performance. The experimental results show that the proposed algorithm has better robustness and classification performance.

Most extant feature selection works neglect interactive features in the form of groups, leading to the omission of some important discriminative information. Moreover, the prevalence of data with uncertainty, fuzziness, and noise poses a certain obstacle to feature selection. Driven by these two issues, a Feature Grouping and Selection approach in Robust Fuzzy Rough Approximation Space using graph theory (FGS-RFRAS) is proposed in this study. First, a robust fuzzy rough approximation space is constructed by a neighborhood adaptive$\beta$-precision fuzzy rough set model to enhance the robustness and antinoise ability of the fuzzy rough set model. Second, uncertainty measures in robust fuzzy rough approximation space are defined to analyze the interactivity and redundancy of pairwise features on graph structure. Then, a strategy ofInteractive Retainment, Weakly Correlated Removal, and Max-Dependent Selectionis devised to guide feature grouping and selection. Experiments are performed on 21 datasets to evaluate the performance of FGS-RFRAS and demonstrate its significance. The robustness test indicates that it is antinoise for mislabeling.

Outlier detection is one of the most important research directions in data mining. However, most of the current research focuses on outlier detection for categorical or numerical attribute data. There are few studies on the outlier detection of mixed attribute data. In this article, we introduce fuzzy rough sets (FRSs) to deal with the problem of outlier detection in mixed attribute data. Since the outlier detection model of the classical rough set is only applicable to the categorical attribute data, we use FRS to generalize the outlier detection model and construct a generalized outlier detection model based on fuzzy rough granules. First, the granule outlier degree (GOD) is defined to characterize the outlier degree of fuzzy rough granules by employing the fuzzy approximation accuracy. Then, the outlier factor based on fuzzy rough granules is constructed by integrating the GOD and the corresponding weights to characterize the outlier degree of objects. Furthermore, the corresponding fuzzy rough granules-based outlier detection (FRGOD) algorithm is designed. The effectiveness of the FRGOD algorithm is evaluated through experiments on 16 real-world datasets. The experimental results show that the algorithm is more flexible for detecting outliers and is suitable for numerical, categorical, and mixed attribute data.

Incremental feature selection approaches can improve the efficiency of feature selection used for dynamic datasets, which has attracted increasing research attention. Nevertheless, there is currently no work on incremental feature selection approaches for dynamic ordered data. Moreover, the monotonic classification effect of ordered data is easily affected by noise, so a robust feature evaluation metric is needed for feature selection algorithm. Motivated by these two issues, we investigate incremental feature selection approaches using a new conditional entropy with robustness for dynamic ordered data in this study. First, we propose a new rough set model, i.e., fuzzy dominance neighborhood rough sets (FDNRS). Second, a conditional entropy with robustness is defined based on FDNRS model, which is used as evaluation metric for features and combined with a heuristic feature selection algorithm. Finally, two incremental feature selection algorithms are designed on the basis of the above researches. Experiments are performed on ten public datasets to evaluate the robustness of the proposed metric and the performance of the incremental algorithms. Experimental results verify that the proposed metric is robust and our incremental algorithms are effective and efficient for updating reducts in dynamic ordered data.

Monotonic classification is a common task in the field of multicriteria decision-making, in which features and decision obey a monotonic constraint. The dominance-based rough set theory is an important mathematical tool for knowledge acquisition in monotonic classification tasks (MCTs). However, existing dominance-based rough set models are very sensitive to noise information, and only a misclassified sample will lead to large errors in acquiring knowledge. This unstable phenomenon does not meet the requirements of practical applications. On the other hand, feature selection is supposedly an effective dimensionality reduction approach for classification tasks. In the real world, feature combinations with multiple correlations can often provide important classification information, where the multiple correlations include redundancy, complementarity, and interaction between features. To the best of our knowledge, most of the existing feature selection methods for MCTs only consider the relevance between features and decision, while ignoring the multiple correlations. To overcome these two drawbacks, in this article, we propose a robust fuzzy dominance rough set model, and develop a feature selection method that considers multiple correlations based on the robust model for MCTs. First, a soft fuzzy dominance rough set (SFDRS) with robustness is proposed. Second, a feature evaluation index considering multiple correlations is presented. Finally, a feature selection algorithm based on SFDRS is designed to select an optimal feature subset. Extensive experiments are conducted on 12 public datasets, and the results show that the SFDRS model has good robustness and the proposed feature selection algorithm has excellent classification performance.

Outlier detection is widely used in many fields, such as intrusion detection, credit card fraud detection, medical diagnosis, and so on. Existing outlier detection algorithms are mostly designed for dealing with numeric or categorical attributes. However, data usually exist in the form of mixed attributes in real-world applications. In this article, we propose a novel mixed attribute outlier detection method based on multigranulation relative entropy by employing the neighborhood rough set. First, the neighborhood system is constructed by optimizing the mixed distance metric and the radius of the statistical value. Second, the neighborhood entropy is introduced as an uncertainty measure of data. Furthermore, the three kinds of multigranulation relative entropy-based matrices are defined by three kinds of attribute sequences, and the multigranulation relative entropy-based outlier factor is integrated to indicate the outlier degree of every object. Based on the proposed outlier detection model, the corresponding algorithm is designed. Finally, the proposed algorithm is compared with other nine algorithms through experiments on public data. The experimental results show that the proposed technique is adaptive and effective.