Multiview Subspace Clustering by an Enhanced Tensor Nuclear Norm

• Published in: IEEE transactions on cybernetics Vol. 52; no. 9; pp. 8962 - 8975
• Main Authors: Xia, Wei, Zhang, Xiangdong, Gao, Quanxue, Shu, Xiaochuang, Han, Jungong, Gao, Xinbo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Clustering; Clustering algorithms; Clustering methods; Coefficients; Correlation; Learning; Mathematical analysis; Matrix decomposition; Minimization; Multiview clustering; Optimization; Periodic structures; Singular value decomposition; spectral clustering; Subspaces; tensor-singular value decomposition (t-SVD); Tensors; weighted nuclear norm
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2021.3052352

Despite the promising preliminary results, tensor-singular value decomposition (t-SVD)-based multiview subspace is incapable of dealing with real problems, such as noise and illumination changes. The major reason is that tensor-nuclear norm minimization (TNNM) used in t-SVD regularizes each singular value equally, which does not make sense in matrix completion and coefficient matrix learning. In this case, the singular values represent different perspectives and should be treated differently. To well exploit the significant difference between singular values, we study the weighted tensor Schatten <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula>-norm based on t-SVD and develop an efficient algorithm to solve the weighted tensor Schatten <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula>-norm minimization (WTSNM) problem. After that, applying WTSNM to learn the coefficient matrix in multiview subspace clustering, we present a novel multiview clustering method by integrating coefficient matrix learning and spectral clustering into a unified framework. The learned coefficient matrix well exploits both the cluster structure and high-order information embedded in multiview views. The extensive experiments indicate the efficiency of our method in six metrics.