Open AccessFast algorithm for large‐scale subspace clustering by LRR
Author(s) -
Xie Deyan,
Nie Feiping,
Gao Quanxue,
Xiao Song
Publication year - 2020
Publication title -
iet image processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.401
H-Index - 45
eISSN - 1751-9667
pISSN - 1751-9659
DOI - 10.1049/iet-ipr.2018.6596
Subject(s) - cluster analysis , computation , algorithm , singular value decomposition , solver , subspace topology , norm (philosophy) , computer science , computational complexity theory , scale (ratio) , matrix norm , mathematics , mathematical optimization , artificial intelligence , eigenvalues and eigenvectors , physics , quantum mechanics , political science , law
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 × n matrix, which leads to a computation complexity of O ( n 3 ) . 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.