Sparse Bayesian Methods for Low-Rank Matrix Estimation

作者：Babacan S Derin^*; Luessi Martin; Molina Rafael; Katsaggelos Aggelos K

来源：IEEE Transactions on Signal Processing, 2012, 60(8): 3964-3977.

DOI：10.1109/TSP.2012.2197748

• Bayesian methods
• low-rankness
• matrix completion
• outlier detection
• robust principal component analysis
• sparse Bayesian learning
• sparsity
• variational Bayesian inference

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. In this paper, we present novel recovery algorithms for estimating low-rank matrices in matrix completion and robust principal component analysis based on sparse Bayesian learning (SBL) principles. Starting from a matrix factorization formulation and enforcing the low-rank constraint in the estimates as a sparsity constraint, we develop an approach that is very effective in determining the correct rank while providing high recovery performance. We provide connections with existing methods in other similar problems and empirical results and comparisons with current state-of-the-art methods that illustrate the effectiveness of this approach.

• 出版日期2012-8
• 单位西北大学