Reweighted Low Rank Representation Based on Fractional-Order Function

Abstract

Low Rank Representation (LRR) achieves state-of-the-art clustering performance via solving a nuclear norm minimization problem which is a convex relaxation of rank minimization. In this paper, we propose a unified fractional-order function based weighted nuclear norm minimization framework (FWNNM), which can approximate rank minimization better than nuclear norm minimization. Based on the unified framework, a fractional-order function is introduced to reweight the low rank representation (FRLRR) to further improve the lower rank representation of data. By imposing constraints on the eigenvalues of coefficient matrix, the proposed weights are embedded into the formulation to obtain the lower rank representation in each iteration. Experimental results demonstrate the advantage of FRLRR over state-of-the-art methods.