Approximate Method of Variational Bayesian Matrix Factorization/Completion with Sparse Prior

TL;DR

This paper presents a variational Bayesian approach for matrix factorization and completion that incorporates sparsity priors, providing analytical solutions and evaluating performance in reconstructing sparse matrices and completing missing data.

Contribution

It introduces an analytical variational Bayesian method for matrix factorization with sparse priors, including approximations and performance evaluation.

Findings

Effective sparse matrix reconstruction demonstrated

Improved matrix completion with sparse priors

Analytical solutions derived for variational Bayesian factorization

Abstract

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We assume the prior of sparse matrix is Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for derivation of matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of sparse matrix reconstruction in matrix factorization, and completion of missing matrix element in matrix completion.