Reweighted Sparse Subspace Clustering Based on Fractional-Order Function

Abstract

Sparse subspace clustering (SSC) achieves state-of-the-art clustering performance via solving a $\ell_{1}$ minimization problem which is a convex relaxation of $\ell_{0}$ minimization. In this paper, we propose a unified fractional-order function based reweighted $\ell_{1}$ minimization framework, which can approximate $\ell_{0}$ norm better than $\ell_{1}$ norm and reweighted $\ell_{1}$ minimization framework. Based on the unified framework, a fractional-order function is introduced to reweight the sparse subspace clustering algorithm (FRSSC) to further improve the sparsity representation of data. By imposing constraints on coefficient matrix, the proposed weights are embedded into the sparse formulation to obtain the sparsest representation in each iteration. Experimental results demonstrate the advantage of FRSSC over state-of-the-art methods.