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Nonconvex low-rank and sparse tensor representation for multi-view subspace clustering

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Abstract

Multi-view subspace clustering has attracted significant attention due to the popularity of multi-view datasets. The effectiveness of the existing multi-view clustering methods highly depends on the quality of the affinity matrix. To derive a high quality affinity matrix, tensor optimization has been explored for multi-view subspace clustering. However, only the global low-rank correlation information among views has been explored, and the local geometric structure has been ignored. In addition, for low-rank tensor approximation learning, the commonly used tensor nuclear norm cannot retain the main information of all views. In this paper, we propose a nonconvex low-rank and sparse tensor representation (NLRSTR) method, which retains the similarity information of the view dimension from global and local perspectives. Specifically, the proposed NLRSTR method imposes nonconvex function and sparse constraint on the self-representation tensor to characterize the high relationship among views. Based on the alternating direction method of multipliers, an effective algorithm is proposed to solve our NLRSTR model. The experimental results on eight datasets show the superiority of the proposed NLRSTR method compared with seventeen state-of-the-art methods.

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Acknowledgements

This work was supported in part by the National Key R&D Program of China 2021YFE0110500, in part by the National Natural Science Foundation of China under Grant 61872034, 62062021,62106063, 62072024 and 62011530042, in part by the Beijing Municipal Natural Science Foundation under Grant 4202055, in part by the RFBR and NSFC according to the research project 20-57-53012 and by project under Grant NoFSFS-2020-0031, in part by the Shenzhen College Stability Support Plan under Grant GXWD20201230155427003-20200824113231001, in part by the Fundamental Research Funds for the Central Universities (2021YJS025).

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Authors and Affiliations

  1. Institute of Information Science, Beijing Jiaotong University, Beijing, China

    Shuqin Wang & Yigang Cen

  2. Beijing Key Laboratory of Advanced Information Science and Network Technology, Beijing, China

    Shuqin Wang & Yigang Cen

  3. School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, China

    Yongyong Chen

  4. College of Mechanical Engineering, Guizhou University, Guiyang, China

    Linna Zhang

  5. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China

    Hengyou Wang

  6. Center for Cognitive Technology and Machine Vision, Moscow State University of Technology “STANKIN”, Moscow, Russian Federation

    Viacheslav Voronin

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  1. Shuqin Wang
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Correspondence to Yigang Cen.

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This article belongs to the Topical Collection: Special Issue on Multi-view Learning

Guest Editors: Guoqing Chao, Xingquan Zhu, Weiping Ding, Jinbo Bi and Shiliang Sun

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Wang, S., Chen, Y., Cen, Y. et al. Nonconvex low-rank and sparse tensor representation for multi-view subspace clustering. Appl Intell 52, 14651–14664 (2022). https://doi.org/10.1007/s10489-022-03406-6

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