Local Weighted Matrix Factorization for Top-n Recommendation with Implicit Feedback

Item recommendation helps people to discover their potentially interested items among large numbers of items. One most common application is to recommend top-n items on implicit feedback datasets (e.g., listening history, watching history or visiting history). In this paper, we assume that the implicit feedback matrix has local property, where the original matrix is not globally low rank but some sub-matrices are low rank. In this paper, we propose Local Weighted Matrix Factorization (LWMF) for top-n recommendation by employing the kernel function to intensify local property and the weight function to model user preferences. The problem of sparsity can also be relieved by sub-matrix factorization in LWMF, since the density of sub-matrices is much higher than the original matrix. We propose a heuristic method to select sub-matrices which approximate the original matrix well. The greedy algorithm has approximation guarantee of factor \(1-\frac{1}{e}\) to get a near-optimal solution. The experimental results on two real datasets show that the recommendation precision and recall of LWMF are both improved about 30% comparing with the best case of weighted matrix factorization (WMF).