Kernelized sparse self-representation for clustering and recommendation

Abstract

Sparse models have demonstrated substantial success in applications for data analysis such as clustering, classification and denois-ing. However, most of the current work is built upon the assumption that data is distributed in a union of subspaces, whereas limited work has been conducted on nonlinear datasets where data reside in a union of manifolds rather than a union of subspaces. To understand data nonlinearity using sparse models, in this paper, we propose to exploit the self-representation property of nonlinear data in an implicit feature space using kernel methods. We propose a ker-nelized sparse self-representation model, denoted as KSSR, and a novel Kernelized Fast Iterative Soft-Thresholding Algorithm, denoted as K-FISTA, to recover the underlying nonlinear structure among the data. We evaluate our method for clustering problems on both synthetic and real-world datasets, and demonstrate its superior performance compared to the other state-of-the-art methods. We also apply our method for collaborative filtering in recommender systems, and demonstrate its great potential for novel applications beyond clustering.