Multiview Subspace Clustering With Grouping Effect

Anchors Crash Tensor: Efficient and Scalable Tensorial Multi-View Subspace Clustering

Tensorial Multi-view Clustering (TMC), a prominent approach in multi-view clustering, leverages low-rank tensor learning to capture high-order correlation among views for consistent clustering structure identification. Despite its promising performance, the TMC algorithms face three key challenges: 1). The severe computational burden makes it difficult for TMC methods to handle large-scale datasets. 2). Estimation bias problem caused by the convex surrogate of the tensor rank. 3). Lack of explicit balance of consistency and complementarity. Being aware of these, we propose a basic framework Efficient and Scalable Tensorial Multi-View Subspace Clustering (ESTMC) for large-scale multi-view clustering. ESTMC integrates anchor representation learning and non-convex function-based low-rank tensor learning with a Generalized Non-convex Tensor Rank (GNTR) into a unified objective function, which enhances the efficiency of the existing subspace-based TMC framework. Furthermore, a novel model ESTMC-C with the proposed Enhanced Tensor Rank (ETR), Consistent Geometric Regularization (CGR), and Tensorial Exclusive Regularization (TER) is extended to balance the learning of consistency and complementarity among views, delivering divisible representations for the clustering task. Efficient iterative optimization algorithms are designed to solve the proposed ESTMC and ESTMC-C, which enjoy time-economical complexity and exhibit theoretical convergence. Extensive experimental results on various datasets demonstrate the superiority of the proposed algorithms as compared to state-of-the-art methods.

GRESS: Grouping Belief-Based Deep Contrastive Subspace Clustering

The self-expressive coefficient plays a crucial role in the self-expressiveness-based subspace clustering method. To enhance the precision of the self-expressive coefficient, we propose a novel deep subspace clustering method, named grouping belief-based deep contrastive subspace clustering (GRESS), which integrates the clustering information and higher-order relationship into the coefficient matrix. Specifically, we develop a deep contrastive subspace clustering module to enhance the learning of both self-expressive coefficients and cluster representations simultaneously. This approach enables the derivation of relatively noiseless self-expressive similarities and cluster-based similarities. To enable interaction between these two types of similarities, we propose a unique grouping belief-based affinity refinement module. This module leverages grouping belief to uncover the higher-order relationships within the similarity matrix, and integrates the well-designed noisy similarity suppression and similarity increment regularization to eliminate redundant connections while complete absent information. Extensive experimental results on four benchmark datasets validate the superiority of our proposed method GRESS over several state-of-the-art methods.

Learning deep representation and discriminative features for clustering of multi-layer networks

The multi-layer network consists of the interactions between different layers, where each layer of the network is depicted as a graph, providing a comprehensive way to model the underlying complex systems. The layer-specific modules of multi-layer networks are critical to understanding the structure and function of the system. However, existing methods fail to characterize and balance the connectivity and specificity of layer-specific modules in networks because of the complicated inter- and intra-coupling of various layers. To address the above issues, a joint learning graph clustering algorithm (DRDF) for detecting layer-specific modules in multi-layer networks is proposed, which simultaneously learns the deep representation and discriminative features. Specifically, DRDF learns the deep representation with deep nonnegative matrix factorization, where the high-order topology of the multi-layer network is gradually and precisely characterized. Moreover, it addresses the specificity of modules with discriminative feature learning, where the intra-class compactness and inter-class separation of pseudo-labels of clusters are explored as self-supervised information, thereby providing a more accurate method to explicitly model the specificity of the multi-layer network. Finally, DRDF balances the connectivity and specificity of layer-specific modules with joint learning, where the overall objective of the graph clustering algorithm and optimization rules are derived. The experiments on ten multi-layer networks showed that DRDF not only outperforms eight baselines on graph clustering but also enhances the robustness of algorithms.