Learning a Joint Low-Rank and Gaussian Model in Matrix Completion with Spectral Regularization and Expectation Maximization Algorithm

Abstract

Completing a partially-known matrix, is an important problem in the field of data science and useful for many related applications, e.g., collaborative filtering for recommendation systems, global positioning in large-scale sensor networks. Low-rank and Gaussian models are two popular classes of models used in matrix completion, both of which have proven success. In this paper, we introduce a single model that leverage the features of both low-rank and Gaussian models. We develop a novel method based on Expectation Maximization (EM) that involves spectral regularization (for low-rank part) as well as maximum likelihood maximization (for learning Gaussian parameters). We also test our framework on real-world movie rating data, and provide comparison results with some of the common methods used for matrix completion.