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 denoising. 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 kernelized 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.