Learning Idempotent Representation for Subspace Clustering

• Published in: IEEE transactions on knowledge and data engineering Vol. 36; no. 3; pp. 1183 - 1197
• Main Authors: Wei, Lai, Liu, Shiteng, Zhou, Rigui, Zhu, Changming, Liu, Jin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Clustering; Clustering algorithms; Coefficients; Computational modeling; Convergence; Critical point; doubly stochastic constraint; idempotent matrix; Laplace equations; normalized membership matrix; Optimization; Reconstruction; Representations; Sparse matrices; Subspace clustering; Subspaces; Synthetic data
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2023.3303343

The critical point for the success of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices that can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix should have two properties: 1) it is block-diagonal with each block indicating a subspace; 2) each block is fully connected. We find that a normalized membership matrix naturally satisfies the above two conditions. Therefore, in this paper, we devise an idempotent representation (IDR) algorithm to pursue reconstruction coefficient matrices approximating normalized membership matrices. IDR designs a new idempotent constraint. And by combining the doubly stochastic constraints, the coefficient matrices which are close to normalized membership matrices could be directly achieved. We present an optimization algorithm for solving IDR problem and analyze its computation burden as well as convergence. The comparisons between IDR and related algorithms show the superiority of IDR. Plentiful experiments conducted on both synthetic and real-world datasets prove that IDR is an effective subspace clustering algorithm.