Subspace clustering via adaptive least square regression with smooth affinities

摘要

It has been proved that subspace clustering algorithms with weighted norm regularizers usually outperform their special cases with non-weighted regularizers. However, it is difficult to design suitable weighted regularizers for different types of subspace clustering algorithms. In this paper, we firstly provide an adaptive weighted norm regularizer construction strategy by using the recently proposed adaptive graph construction method. Secondly, we give a proposition that the affinities obtained by the adaptive graph construction method should be changed smoothly on the original data manifold. Hence, we devise a graph-constraint for the obtained affinity matrix. Thirdly, by integrating the above two techniques and least square regression (LSR) algorithm together, we design a new subspace clustering algorithm, called adaptive least square regression with smooth affinities (ALSR). For solving ALSR problem, we present an optimization algorithm whose computation burden and convergence are analyzed. Finally, plentiful experiments conducted on different types databases show the superiorities of ALSR.