A Family of Non-negative Matrix Factorizations for One-Class Collaborative Filtering Problems
Vikas Sindhwani, Serhat S. Bucak, Jun Hu, Aleksandra Mojsilović · 2009
This paper is motivated by the industrial research problem of designing a real-world recommender system for a large Information Technology (IT) company. Given historical records of client purchases, compactly represented as a sparse client-times-product “who-bought-what ” binary matrix, the goal is to build a model that provides recommendations for what products should be sold next to the existing client base. Such a problem may naturally be formulated as a collaborative filtering task. However, this is a one-class setting, that is, if a client has not bought a product yet, it does not imply that the client has a low propensity to potentially buy that product later. In the absence of explicitly labeled negative examples, one may resort to considering zero-valued client-product pairs as either missing data or as surrogate negative instances. In this paper, we outline an approach to explicitly deal with this kind of ambiguity by instead treating zero-valued pairs as optimization variables. These variables are optimized in conjunction with learning a weighted, low-rank non-negative matrix factorization (NMF) of the client-product matrix. The proposed algorithm alternates NMF optimization with deterministicannealing/continuation techniques designed for global minimization of combinatorial and non-convex objective functions. Experimental results show that our approach can give significantly better recommendations in comparison to various competing alternatives on a one-class collaborative filtering task.