Exploiting Feature Information in Matrix Completion

• Activity Number: 611
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Anran Wang*+ and Hua Zhou and Lexin Li
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: genotype imputation ; graph Laplacian ; matrix completion ; Nesterov method ; nuclear norm ; spectral regularization

Abstract

Matrix completion aims to recover a large matrix of which only a small fraction of entries are observed. An archetypal example is the Netflix challenge, where viewers (rows) only rate a small number of movies (columns) and the goal is to impute unobserved entries of the viewer-movie rating matrix so to predict the ratings of movies that viewers have not yet rated. In many such applications, in addition to the observed matrix entries, abundant feature information is available. In the Netflix example, viewers' demographic information and the movies' background information were present along with the observed ratings. In this article, we propose a general regularization solution that simultaneously exploits both the low rank matrix structure and the rich feature information. Our solution integrates two types of regularizations, spectral and graph Laplacian regularizations, and can be viewed as a matrix version of the popular elastic net regularization. We develop highly efficient computational algorithms which have explicit convergence rates and are scalable to remarkably big data sets. Simulations and two real data analysis demonstrate the superior performance of the proposed method.