Bilateral Fast Low-Rank Representation With Equivalent Transformation for Subspace Clustering

Abstract

In recent years, low-rank representation (LRR) has received increasing attention on subspace clustering. Due to inevitable matrix inversion and singular value decomposition in each iteration, however, most of existing LRR algorithms may suffer from high computational complexity, and hence can not cope with the large-scale sample data commendably. To overcome this problem, in this paper, we propose a bilateral fast low-rank representation (BFLRR), which has a linear time complexity with respect to the number of samples. Specifically, we introduce the equivalent transformation method to remove the null spaces of both the columns and rows of the coefficient matrix so that a hypercompact coefficient matrix can be learned. Furthermore, the proposed BFLRR is embedded into a distributed framework as DFC-BFLRR to make it more efficient, which utilizes a combination of the global and local projection matrices. Extensive experiments are carried out on real datasets, and the results testify that the proposed methods not only perform faster-computing speed but also obtain favorable clustering accuracy in comparison with the competing methods among large-scale sample data.