Local Low-Rank Matrix Approximation with Preference Selection of Anchor Points

Abstract

Matrix factorization is widely used in personalized recommender systems, text mining, and computer vision. A general assumption to construct matrix approximation is that the original matrix is of global low rank, while Joonseok Lee et al. proposed that many real matrices may be not globally low rank, and thus a locally low-rank matrix approximation method has been proposed.[11] However, this kind of matrix approximation method still leaves some important issues unsolved, for example, the randomly selecting anchor nodes. In this paper, we study the problem of the selection of anchor nodes to enhance locally low-rank matrix approximation. We propose a new model for local low-rank matrix approximation which selects anchor-points using a heuristic method. Our experiments indicate that the proposed method outperforms many state-of-the-art recommendation methods. Moreover, the proposed method can significantly improve algorithm efficiency, and it is easy to parallelize. These traits make it potential for large scale real-world recommender systems.