Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices

2009/05/02 by John Wright, Arvind Ganesh, Wright, John +5 · 115 citations
Chemistry · Computer Science · Engineering · Mathematics · #Algorithm #Blind Source Separation Techniques #Combinatorics #Component (thermodynamics) #Computer science #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematics #Physics #Principal component analysis #Rank (graph theory) #Robust principal component analysis #Sparse and Compressive Sensing Techniques #Spectroscopy and Chemometric Analyses #Statistics #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.0905.0233

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2009/05/02 · arxiv created 2009/12/09 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper has been withdrawn due to a critical error near equation (71). This error causes the entire argument of the paper to collapse. Emmanuel Candes of Stanford discovered the error, and has suggested a correct analysis, which will be reported in a separate publication.

Citations

• The Approximation of One Matrix by Another of Lower Rank
• Atomic Decomposition by Basis Pursuit
• Random sample consensus
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• A Singular Value Thresholding Algorithm for Matrix Completion
• Matrix Completion With Noise

Cited by

• Matrix Completion from Noisy Entries

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• Stable Principal Component Pursuit
• Robust principal component analysis?
• Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
• RES-PCA: A Scalable Approach to Recovering Low-rank Matrices
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