A Continuous Weighted Low-Rank Approximation for Collaborative Filtering Problems

Collaborative filtering is a recent technique that recommends products to customers using other users' preference data. The performance of a collaborative filtering system generally degrades when the number of customers and products increases, hence the dimensionality of filtering database needs to be reduced. In this paper, we discuss the use of weighted low rank matrix approximation to reduce the dimensionality of a partially known dataset in a collaborative filtering system. Particularly, we introduce a projected gradient flow approach to compute a weighted low rank approximation of the dataset matrix.