Low-Rank Matrix Recovery With Simultaneous Presence Of Outliers And Sparse Corruption

Keywords

big data; data sketching; matrix decomposition; outlier detection; randomization; Robust PCA; sparse corruption; sparse matrix; subspace learning; unsupervised learning

Abstract

We study a data model in which the data matrix D ∈ ℝN1 × N2 can be expressed as D = L + S + C, where L is a low-rank matrix, S is an elementwise sparse matrix, and C is a matrix whose nonzero columns are outlying data points. To date, robust principal component analysis (PCA) algorithms have solely considered models with either S or C, but not both. As such, existing algorithms cannot account for simultaneous elementwise and columnwise corruptions. In this paper, a new robust PCA algorithm that is robust to simultaneous types of corruption is proposed. Our approach hinges on the sparse approximation of a sparsely corrupted column so that the sparse expansion of a column with respect to the other data points is used to distinguish a sparsely corrupted inlier column from an outlying data point. We also develop a randomized design that provides a scalable implementation of the proposed approach. The core idea of sparse approximation is analyzed analytically where we show that the underlying ℓ1-norm minimization can obtain the representation of an inlier in presence of sparse corruptions.

Publication Date

12-1-2018

Publication Title

IEEE Journal on Selected Topics in Signal Processing

Volume

12

Issue

6

Number of Pages

1170-1181

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/JSTSP.2018.2876604

Socpus ID

85055148671 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85055148671

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