A Collaborative Filtering Model: Statistical Properties of Alternating Least Squares

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, based on their previous ratings. The objective of the recommender system is to obtain a model that predicts future ratings a user might give for a specific movie. One such model is known as a collaborative filtering model. When applied to movie selection, the model includes the average movie rating (μ), the rating bias of the user (b), the overall popularity of the movie (a), and the interaction between user preferences (p) and movie characteristics (q). The collaborative filtering model makes use of the sparse data collected from users who have watched movies and provided ratings. With the data, the model obtains predicted ratings for movies the users have not yet watched. Collaborative filtering models have had growing interest recently due to the Netflix million-dollar challenge to improve its existing algorithm for recommending movies. Through the contest, Netflix hoped to enhance the method with which they recommend movies to their users. This method would be based on prior movies the users have rated. The goal of the contest was to predict, as accurately as possible, what any particular user would rate a movie.