Sparse additive subspace clustering

Abstract

In this paper, we introduce and investigate a sparse additive model for subspace clustering problems. Our approach, named SASC (Sparse Additive Subspace Clustering), is essentially a functional extension of the Sparse Subspace Clustering (SSC) of Elhamifar & Vidal [7] to the additive nonparametric setting. To make our model computationally tractable, we express SASC in terms of a finite set of basis functions, and thus the formulated model can be estimated via solving a sequence of grouped Lasso optimization problems. We provide theoretical guarantees on the subspace recovery performance of our model. Empirical results on synthetic and real data demonstrate the effectiveness of SASC for clustering noisy data points into their original subspaces. © 2014 Springer International Publishing.