Sciweavers

Share
SIAMJO
2011

Rank-Sparsity Incoherence for Matrix Decomposition

10 years 2 months ago
Rank-Sparsity Incoherence for Matrix Decomposition
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is NP-hard in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the 1 norm and the nuclear norm of the components. We develop a notion of rank-sparsity incoherence, expressed as an uncertainty principle between the sparsity pattern of a matrix and its row and column spaces, and use it to characterize both fundamental identifiability as well as (deterministic) sufficient conditions for exact recovery. Our analysis is geometric in nature, with the tangent spaces to the algebraic varieties of sparse and low-rank matrices playing a prominent role. When the sparse and low-rank matrices are drawn fro...
Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Pa
Added 17 Sep 2011
Updated 17 Sep 2011
Type Journal
Year 2011
Where SIAMJO
Authors Venkat Chandrasekaran, Sujay Sanghavi, Pablo A. Parrilo, Alan S. Willsky
Comments (0)
books