Robust subspace clustering via multi-affinity matrices fusion

Abstract

Subspace clustering (SC) methods have attracted widespread attention from interested researchers, and a variety of SC methods have been proposed recently. In general, SC methods obtain an affinity matrix, on which spectral clustering is used. Obviously, affinity matrices obtained by different algorithms are not the same, and their clustering effects are also different. A question then arises of whether the affinity matrices obtained by different algorithms can be merged to improve the clustering performance. The answer may be yes I n this paper, we design a new SC method, i.e., robust subspace clustering via multi-affinity matrices fusion (RSC/MAMF). Specifically, several classical SC algorithms, i.e., sparse subspace clustering (SSC), low-rank representation (LRR) and least squares regression (LSR), are first chosen to derive their own affinity matrices. To make full use of the information of different affinity matrices, and to mine the subspace structure thoroughly, we further fuse the derived affinity matrices, i.e., splice them into a 3-order tensor, and impose a weighted tensor nuclear norm (WTNN) to it, which not only mines and fuses the information of the different affinity matrices but also removes their noise. Additionally, to further explore the consistency of the different affinity matrices, spectral embedding is also unified into the final objective function. We propose an optimization algorithm to address the optimization problem of RSC/MAMF, which utilizes the Augmented Lagrange Multiplier (ALM) method. Experiments show that the multi-affinity matrices fusion idea is feasible, and RSC/MAMF outperforms the state-of-the-art SC methods.