Fast algorithm for large-scale subspace clustering by LRR

• Published in: IET image processing Vol. 14; no. 8; pp. 1475 - 1480
• Main Authors: Xie, Deyan, Nie, Feiping, Gao, Quanxue, Xiao, Song
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 19.06.2020
• Subjects: Caltech101 databse; computation complexity; computational complexity; large‐scale problem; large‐scale subspace clustering; low‐rank representation; matrix algebra; MNIST; original LRR solver; pattern clustering; Research Article; singular value decomposition; small‐scale problem; subspace clustering problems; traditional LRR algorithm; traditional LRR algorithm; MNIST; matrix algebra; original LRR solver; Caltech101 databse; large-scale subspace clustering; computation complexity; subspace clustering problems; pattern clustering; low-rank representation; large-scale problem; small-scale problem; singular value decomposition; computational complexity
• ISSN: 1751-9659; 1751-9667; 1751-9667
• DOI: 10.1049/iet-ipr.2018.6596

Low-rank representation (LRR) and its variants have been proved to be powerful tools for handling subspace clustering problems. Most of these methods involve a sub-problem of computing the singular value decomposition of an $n \times n$n×n matrix, which leads to a computation complexity of $O(n^3)$O(n3). Obviously, when n is large, it will be time consuming. To address this problem, the authors introduce a fast solution, which reformulates the large-scale problem to an equal form with smaller size. Thus, the proposed method remarkably reduces the computation complexity by solving a small-scale problem. Theoretical analysis proves the efficiency of the proposed model. Furthermore, we extend LRR to a general model by using Schatten p-norm instead of nuclear norm and present a fast algorithm to solve large-scale problem. Experiments on MNIST and Caltech101 databse illustrate the equivalence of the proposed algorithm and the original LRR solver. Experimental results show that the proposed algorithm is remarkably faster than traditional LRR algorithm, especially in the case of large sample number.