稳健主成分分析
秩(图论)
约束(计算机辅助设计)
矩阵分解
稀疏PCA
稀疏矩阵
计算机科学
低秩近似
贝叶斯概率
矩阵完成
主成分分析
基质(化学分析)
算法
数学优化
人工智能
数学
特征向量
组合数学
物理
数学分析
复合材料
高斯分布
量子力学
材料科学
汉克尔矩阵
几何学
作者
S. Derin Babacan,Martin Luessi,Rafael Molina,Aggelos K. Katsaggelos
标识
DOI:10.1109/tsp.2012.2197748
摘要
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.
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