Sparse Bayesian Methods for Low-Rank Matrix Estimation

By S. D. Babacan, Martin Luessi, Rafael Molina, Aggelos K. Katsaggelos. IEEE Transactions on Signal Processing, 2011

304 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/7b71acff127c9bc736185343221f05aac4768ac0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. Thierry Bouwmans
2. Wangmeng Zuo
3. Deyu Meng
4. Qi Xie
5. Soon Ki Jung
6. Xiangchu Feng
7. Shuhang Gu
8. Shinichi Nakajima

In Computational Mechanics

1. Wangmeng Zuo
2. Lei Zhang
3. Xiangchu Feng
4. Deyu Meng
5. Thierry Bouwmans
6. Shuhang Gu
7. Qian Zhao
8. Qi Xie

In Signal Processing

1. Masashi Sugiyama
2. Thierry Bouwmans
3. Xiangchu Feng
4. Qibin Zhao
5. Liqing Zhang
6. S. D. Babacan
7. Andrzej S. Cichocki
8. Wangmeng Zuo

Citations in the corpus

• Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination (2014, methodology): “Probabilistic matrix factorization was proposed in [27], and its fully Bayesian treatment using Markow chain Monte Carlo (MCMC) inference was shown in [28] and using variational Bayesian inference in [29], [30].”
• Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “35http://winsty.net/prmf.html Title Suppressed Due to Excessive Length 103 Experimental results [435] on the SABS dataset [40] show that MBRMF outperforms PCP solved via IALM [45], BRPCA [83], VBRPCA [18], DECOLOR [464] and PRMF [385].”
• Global analytic solution of fully-observed variational Bayesian matrix factorization (2013, background): “Its VB variant has also been proposed (Babacan et al., 2012).”
• Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, methodology): “Bayesian RPCA approaches have also been investigated in [2], [15], [75].”
• Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “These probabilistic methods are capable of adapting different kinds of noises, such as dense noise with Gaussian distribution (Tipping and Bishop 1999; Mnih and Salakhutdinov 2007), sparse noise distribution (Wang and Yeung 2013; Babacan et al. 2012; Ding et al. 2011) and more complex mixture-ofGaus”
• Traditional and recent approaches in background modeling for foreground detection: An overview (2014, methodology): “This method has been improved in a variational Bayesian framework [13].”