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multi-view subspace clustering via slack consistency and double-side orthogonal diversity

EXPERT SYSTEMS WITH APPLICATIONS 2025年 277卷

作者： Luo, Yixuan Ma, Wenming Liu, Shudong Tong, Xiangrong Du, Xiaolin Liu, Zhaowei Li, Mingqi Jiang, Hongwei Yantai Univ Sch Comp & Control Engn Yantai 264005 Peoples R China Zhongnan Univ Econ & Law Sch Informat Engn Wuhan 2430073 Peoples R China

multi-view subspace clustering is a powerful technique for handling high-dimensional data and effectively reducing dimensionality. However, current multi-view subspace clustering methods encounter two significant challenges. First, they heavily rely on the self-representation matrix to extract consistency information between views, which may introduce noise and lead to overly constrained consistency matrices. Second, existing methods struggle to balance consistency and complementarity in multi-view clustering. To address these issues, we propose a novel multi-view subspace clustering approach based on slack consistency and double- side orthogonal diversity (SCDOD). Our method introduces a set of slack consistency matrices that bridge the self-representation matrix and the global consistency matrix. Through global consistency constraints, we obtain global consistency information while mitigating constraints typically associated with global consistency construction. Additionally, our approach incorporates double-side orthogonal diversity, enhancing diversity between the slack consistency matrices and specificity matrices, as well as among the specificity matrices themselves. This effectively explores the complementarity of different data views. Experimental results on several real-world datasets demonstrate the effectiveness of our proposed method.

关键词： multi-view subspace clustering Low-rank tensor constraint Orthogonal diversity Slack consistency

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BACVC: Bi-adaptive and cross-view consistency for incomplete multi-view subspace clustering

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ALEXANDRIA ENGINEERING JOURNAL 2025年 119卷 623-633页

作者： Zhan, Jiaqiyu Zhu, Yuesheng Luo, Guibo Peking Univ Sch Elect & Comp Engn Shenzhen Grad Sch Shenzhen Peoples R China

multi-view subspace clustering leverages complementary information from different views to uncover latent subspaces. However, incomplete multi-view data is prevalent, particularly infields such as communication systems. Incomplete multi-view subspace clustering (IMSC) addresses this challenge but faces two main challenges: (1) neglecting dissimilarities between views and samples, and (2) insufficient handling of cross- view consistency. To tackle these issues, we propose a novel IMSC framework, referred to as Bi-Adaptive and Cross-view Consistency (BACVC). BACVC improves incomplete data recovery and subspace structure discovery through view-adaptive tensor rank constraints, data-adaptive high-order correlations, and viewlevel contrastive learning. Specifically, we first apply tensor factorization with view-adaptive tensor rank approximation to enforce low-rank constraints on a stacked affinity tensor, capturing the view-specific subspace block-diagonal structure. We then introduce a data-adaptive non-uniform hypergraph-induced hyper-Laplacian regularization to model high-order correlations and guide the recovery of incomplete data. Finally, contrastive learning is applied to the soft clustering assignment of each view, ensuring cross-view structural consistency. Extensive experiments on four benchmark datasets show that BACVC outperforms eleven state-of-the-art methods, with improvements of up to 4.39%, 5.43%, and 3.95% in ACC, NMI, and purity, respectively. Experimental results demonstrate the robustness of BACVC in handling incomplete data and its effectiveness in practical applications.

关键词： multi-view subspace clustering Incomplete multi-view data High-order correlation Tensor factorization Contrastive learning

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Consistency and Diversity Induced Tensorized multi-view subspace clustering

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2025年第1期9卷 798-809页

作者： Xiao, Chunming Huang, Yonghui Huang, Haonan Zhao, Qibin Zhou, Guoxu Guangdong Univ Technol Sch Automat Key Lab Intelligent Detect & Internet Things Mfg Minist Educ Guangzhou 510006 Peoples R China Guangdong Univ Technol Sch Automat Guangdong Key Lab IoT Informat Technol Guangzhou 510006 Peoples R China RIKEN Ctr Adv Intelligence Project AIP Tokyo 1030027 Japan Guangdong Univ Technol Sch Automat Guangzhou Peoples R China Guangdong Univ Technol Ctr Intelligent Batch Mfg Based IoT Technol 111 Sch Automat Guangzhou 510006 Peoples R China

Tensorizedmulti-view subspace clustering has attracted intensive attention to achieve promising clustering performance by effectively modeling both consistency and high-order correlation structure from multiple views. However, existing tensorized multi-view subspace clustering methods often neglect the prevalent diversity among different views, which are specific attributes unique to each view. In this paper, we focus on simultaneously exploiting the multi-view consistency and diversity information in a tensorized multi-view subspace framework. In the diversity part, an additional position-aware exclusivity term is introduced to explore the unique features of each view to enhance feature complementarity between different views. Meanwhile, we explore inter-view similarity by minimizing the tensor Schatten p-norm, which well captures both consistency and high-order correlation information of multi-view data. Then, the objective function can be efficiently optimized by the alternating direction method of multipliers. Extensive experiments on eight benchmark datasets demonstrate that the proposed method outperforms the state-of-the-art multi-view clustering methods.

关键词： Tensors Correlation Data models Automation Matrix decomposition Linear programming clustering methods Consistency diversity multi-view subspace clustering p-norm tensor

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multi-view subspace clustering with a consensus tensorized scaled simplex representation

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INFORMATION SCIENCES 2025年 695卷

作者： He, Hao Cai, Bing Wang, Xinyu Anhui Inst Informat Technol Sch Comp & Software Engn Wuhu 241000 Peoples R China Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Peoples R China

multi-view clustering has been at the forefront of research focused on identifying an ideal structure for the rational partitioning of sample points. multi-view clustering faces two main challenges: identifying the optimal structure within each view and fusing these structures into a reliable consensus matrix. To overcome these obstacles, we introduce the Consensus Tensorized Scaled Simplex Representation (CTSSR). First, CTSSR uses the scaled simplex representation to reveal the structure within each view flexibly. Second, we apply a rank constraint strategy to ensure that the learned subspace structure embodies the optimal clustering structure. To fuse multiple views, we propose a normalized view weighting mechanism based on each view's reconstruction error, ensuring reasonable contributions to the consensus matrix. Finally, we employ tensor learning on weighted subspace views to explore high-order correlations and subtle differences between views, refining the exploration of inter-view relationships. CTSSR combines intra-view structure exploration with inter-view relationship analysis, resulting in an ideal consensus matrix. It shows excellent clustering performance on real-life datasets, significantly outperforming state-of-the-art methods in various experimental settings.

关键词： multi-view subspace clustering Scaled simplex representation Rank constraint Tensor learning

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Consistency and inconsistency guided multi-view subspace clustering based on low-rank tensor and comprehensive similarity

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KNOWLEDGE-BASED SYSTEMS 2025年 318卷

作者： Yan, Yutong Chen, Hongmei Yin, Tengyu Mi, Yong Horng, Shi-Jinn Li, Tianrui Southwest Jiaotong Univ Sch Comp & Artificial Intelligence Chengdu 611756 Peoples R China Southwest Jiaotong Univ Natl Engn Lab Integrated Transportat Big Data Appl Chengdu 611756 Peoples R China Minist Educ Engn Res Ctr Sustainable Urban Intelligent Transpo Chengdu 611756 Peoples R China Southwest Jiaotong Univ Mfg Ind Chains Collaborat & Informat Support Techn Chengdu 611756 Peoples R China Asia Univ Dept Comp Sci & Informat Engn Taichung 41354 Taiwan China Med Univ China Med Univ Hosp Dept Med Res Taichung 404327 Taiwan

multi-view subspace clustering methods have gained significant attention in recent years owing to their ability to explore the data's low-dimensional subspace structure. Most existing subspace clustering methods focus on learning consensus and specific representations under the self-representation principle, but there are still two shortcomings. First, subspace clustering methods usually neglect preserving the local structure of the data. While a few methods notice this, they construct predefined similarity graphs by measuring the Euclidean distance of sample pairs, which cannot sufficiently capture the local structure of the data information. Secondly, some methods ignore the high-order information between views. This study proposes a multi-view clustering method called consistency and inconsistency-guided multi-view subspace clustering based on low-rank tensor and comprehensive similarity (CIMSC-LTCS) to overcome these shortcomings. In particular, we decompose the self-representation matrix of each view into the consistent part and the inconsistent part to explicitly capture cross-view consistency and inconsistency. Further, the high-order information between views of the consistent representation is explored by low-rank tensor learning. Moreover, the optimal comprehensive consensus similarity graph is adaptively learned by simultaneously considering the direct similarity relation and latent similarity relation between sample pairs, and the comprehensive consensus similarity graph is used to guide the learning of the consistent representation matrices to preserve the local structure of the data better. The method integrates consistency and inconsistency decomposition, comprehensive similarity learning, and low-rank representation tensor learning into one framework. Finally, extensive experiments are conducted on fifteen benchmark multi-view datasets, which demonstrate the superiority of the proposed method.

关键词： multi-view subspace clustering Consistent representation Low-rank tensor Latent similarity

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Large-scale multi-view subspace clustering with latent centroid anchor guidance

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multiMEDIA SYSTEMS 2025年第3期31卷 1-16页

作者： Han, Chengming Wu, Zikai Zhang, Hongjuan Dong, Anxue Univ Shanghai Sci & Technol Business Sch Shanghai 200093 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

multi-view subspace clustering (MVSC) is a crucial and widely used method, as it effectively combines multi-view data to uncover significant patterns. However, its high computational cost limits its application to large-scale datasets. To address this, Anchor-based MVSC methods have been proposed, with adaptive anchor point selection being the most popular. However, these methods still have room for improvement in three areas: (1) most adaptive anchor selection methods learn anchors and construct anchor graphs in the original space, where redundancy and noise are inevitable, especially in high-dimensional data. (2) Adaptive anchor selection methods often result in anchors that lack representativeness and are unevenly distributed. (3) Existing methods always fail to consider the overall structure of the dataset during anchor learning. To address these issues, we propose a new multi-view subspace clustering method called Large-Scale multi-view subspace clustering with Latent Centroid Anchor Guidance (MVSC-LCA). Specifically, we integrate latent intact space learning, anchor search, and anchor graph construction into a unified framework, achieving mutual reinforcement and joint optimization. Unlike existing methods that learn anchors and construct anchor graphs in the original space, we perform anchor learning and graph construction in the latent intact space. Additionally, we design a novel regularization term that drives the anchor set towards the latent centroid, thereby fully leveraging the overall structure of the dataset during the anchor learning process, making the anchor set more representative. Finally, extensive experiments on eight benchmark datasets with large-scale data demonstrate the effectiveness and superiority of MVSC-LCA existing state-of-the-art clustering methods.

关键词： multi-view subspace clustering Anchor-based MVSC methods Adaptive anchor High-quality anchor graph

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Adaptive multi-view subspace clustering algorithm based on representative features and redundant instances

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NEUROCOMPUTING 2025年 620卷

作者： Ou, Zhuoyue Deng, Xiuqin Chen, Lei Deng, Jiadi Guangdong Univ Technol Sch Math & Stat 161 Yinglong Rd Guangzhou Peoples R China

The goal of multi-view subspace clustering is to group objects into distinct clusters using information from multiple views, which remains challenging when dealing with diverse data sources. However, the learned consensus matrix of most of the existing approaches maybe inaccurate and lead to unsatisfactory clustering performance due to the following two limitations. The first one is that the representative features are treated equally with the other unimportant features, thus resulting in the incapability of capturing the latent information in each view. Second, the redundant information is not considered from the viewpoints, which raises a negative impact caused by certain noise. This paper proposes a novel adaptive multi-view subspace clustering based on representative features and redundant instances (AMC2R) to address these two challenging issues. Specifically, the proposed algorithm focuses on the representative feature, in which a weighted matrix is designed for each view to dynamically obtain a consensus matrix using the information conveyed by each feature. After that, all the views are concatenated together to utilize the complementary information across the views, and a matrix under l 2 , 1-norm constraint is used to obtain the final consensus matrix to eliminate the negative impact raised by the redundant information. A unified framework is then designed to integrate the above steps. In this way, the representative information and the redundant information can simultaneously interact with one another during the iterations. Experimental results on different datasets demonstrate the effectiveness of the proposed algorithm and have achieved excellent results on Accuracy (ACC), Normalized Mutual Information (NMI), and Adjusted Rand Index (ARI).

关键词： multi-view subspace clustering Representative features Redundant instances Auto-weighted mechanism l2, 1-norm

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Tensorial multi-view subspace clustering based on logarithmic n-order penalty

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PATTERN RECOGNITION 2025年 162卷

作者： Liu, Chang Zhang, Hongbing Fan, Hongtao Li, Yajing Northwest A&F Univ Coll Sci Yangling 712100 Shaanxi Peoples R China Lanzhou Univ Sch Math & Stat Lanzhou 730000 Peoples R China

The low-rank tensor can demonstrate the internal features of the data and explore the higher-order correlations between multi-view data, and has been successfully used in multi-view clustering. However, most of the existing methods use the tensor nuclear norm (TNN) as a convex approximation of the tensor rank function. The TNN approach applies the same weight information to all singular values, which usually leads to a sub-optimal tensor representation. In this paper, anew non-convex logarithmic n-order penalty (LNP) function is designed, which can fully take into account the differences existing between different singular values. What is more, a tensorial multi-view subspace clustering model about LNP (LNP-TMSC) is proposed. The norm based on LNP can integrate the structural information encoded by larger singular values. Thus amore compact tensor with LR properties can be learned that can fully preserve the consistency between views and explore the high- order correlation. The proposed model is solved using the alternating direction method of multipliers and the resulting algorithm is proved theoretically to converge to a Karush-Kuhn-Tucker point. The experimental results demonstrate the validity and superiority of the LNP-TMSC model.

关键词： Logarithmic n-order penalty multi-view subspace clustering Non-convex optimization Theoretical convergence

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Robust multi-view subspace clustering via neighbor embedding on manifold and low-rank representation learning

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 267卷

作者： Kong, Jiarui Liu, Jingya Shang, Ronghua Zhang, Weitong Xu, Songhua Li, Yangyang Xidian Univ Sch Artificial Intelligence Key Lab Intelligent Percept & Image Understanding Minist Educ Xian 710071 Shaanxi Peoples R China Xi An Jiao Tong Univ Dept Hlth Management Affiliated Hosp 2 Xian 710004 Shaanxi Peoples R China Xi An Jiao Tong Univ Inst Med Artificial Intelligence Affiliated Hosp 2 Xian 710004 Shaanxi Peoples R China

multi-view subspace clustering is the most widespread method of multi-view clustering. However, most existing multi-view subspace clustering approaches posit that high-dimensional data are distributed in the linear lower- dimensional subspace, which is not suitable to the case of manifold data embedding. To address this challenge, we propose a novel robust multi-view subspace clustering approach via neighbor embedding on manifold and low-rank representation learning (NELR). Specifically, NELR explores the underlying local connectivity information utilizing the nearest neighbor, and then the connectivity matrix is constructed by the neighborhood expanding. The learned connectivity matrix well leverages the local neighborhood information among the data points and simultaneously reveals the structure of the manifold. After that, NELR exploits the learned connectivity matrix as a special linear graph convolution into the construction of multi-view self-representation matrix, and accordingly composes more robust graph embedding dictionaries on the multi views. Moreover, to well facilitate the consensus and low rank representation, NELR jointly imposes the low-rank constraint and pairwise constraint on the construction. The experiments on seven datasets demonstrate that the clustering accuracy and standard mutual information of NELR are better than eight compared algorithms. The code for NELR can be obtained at https://***/KKJerry/NELR.

关键词： multi-view subspace clustering Neighborhood expanding Low-rank representation Graph convolution

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Specific and coupled double consistency multi-view subspace clustering with low-rank tensor learning

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SIGNAL PROCESSING 2025年 229卷

作者： Wu, Tong Lu, Gui-Fu Anhui Polytech Univ Sch Comp & Informat Wuhu 241000 Anhui Peoples R China

multi-view clustering (MVC) has gained widespread attention due to its ability to utilize different features from different views. However, the existing MVC methods fail to fully exploit the consistency across multiple views, leading to information loss. Additionally, the performance of the algorithms is not satisfactory due to the inherent noise in the data. To address the above-mentioned issues, this paper proposes the specific and coupled double consistency multi-view subspace clustering with low-rank tensor learning (SCDCMV) method. Specifically, firstly, we simultaneously incorporate the consistency and specificity of multiple views into self-expressive learning. However, the information within the consistency matrix has not been fully utilized, and there still exists some noise. Then, the obtained consistency matrix is once again integrated into self-expressive learning to obtain a new consistency matrix. Thirdly, we combine the two consistency matrices into a tensor and constrain it using tensor nuclear norm (TNN). Then, under the constraint of TNN, the two consistency matrices mutually reinforce each other, which helps fully utilize the consistency information and reduce the impact of noise, ultimately leading to better clustering results. Ultimately, these three steps constitute a framework that is tackled utilizing the augmented Lagrange multiplier method. The performance of SCDCMV has improved by 55.94 %. Experimental results on different datasets indicate that the SCDCMV algorithm outperforms state-of-the-art algorithms. In other words, these experimental results validate the importance of effectively utilizing consistent information from multiple views while reducing the impact of noise. The code is publicly available at https://***/To ngWuahpu/SCDCMV.

关键词： Consistency Specificity Tensor nuclear norm multi-view subspace clustering

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