Parallelization of Matrix Factorization for Recommender Systems

Abstract

Recommender systems are emerging as important tools for improving customer satisfaction by mathematically predicting user preferences. Several major corporations including Amazon.com and Pandora use these types of systems to suggest additional options based on current or recent purchases. Netflix uses a recommender system to provide its customers with suggestions for movies that they may like, which are based on their previous ratings. In 2006, Netflix released a large data set to the public and offered one million dollars for significant improvements on their system. In 2009, BellKor’s Pragmatic Chaos, a team of seven, won the prize by combining individual methods. Dr. Robert Bell, with whom we collaborated, was a member of the winning team and provided us with the data set used in this project, consisting of a sparse matrix with rows of users and columns of movies. The entries of the matrix are ratings given to movies by certain users. The objective is to obtain a model that predicts future ratings a user might give for a specific movie. This model is known as a collaborative filtering model, which encompasses the average movie rating (mu), the rating bias of the user (b), the overall popularity of a movie (a), and the interaction between user preferences (p) and movie characteristics (q). Two methods, Alternating Least Squares and Stochastic Gradient Descent, were used to estimate each parameter in this non-linear regression model. Each method fits characteristic vectors for movies and users from the existing data. The overall focus of this project is to explore the two methods, and to investigate the suitability of parallel computing utilizing the cluster Tara in the UMBC High Performance Computing Facility.