Fast algorithm for large‐scale subspace clustering by LRR

Abstract

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.