Robust Subspace Clustering With Independent and Piecewise Identically Distributed Noise Modeling

Abstract

Most of the existing subspace clustering (SC) frameworks assume that the noise contaminating the data is generated by an independent and identically distributed (i.i.d.) source, where the Gaussianity is often imposed. Though these assumptions greatly simplify the underlying problems, they do not hold in many real-world applications. For instance, in face clustering, the noise is usually caused by random occlusions, local variations and unconstrained illuminations, which is essentially structural and hence satisfies neither the i.i.d. property nor the Gaussianity. In this work, we propose an independent and piecewise identically distributed (i.p.i.d.) noise model, where the i.i.d. property only holds locally. We demonstrate that the i.p.i.d. model better characterizes the noise encountered in practical scenarios, and accommodates the traditional i.i.d. model as a special case. Assisted by this generalized noise model, we design an information theoretic learning (ITL) framework for robust SC through a novel minimum weighted error entropy (MWEE) criterion. Extensive experimental results show that our proposed SC scheme significantly outperforms the state-of-the-art competing algorithms.