Robust Principal Component Analysis with Non-Sparse Errors

Jushan Bai; Junlong Feng

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arXiv · 1902.08735

Robust Principal Component Analysis with Non-Sparse Errors

Jushan Bai·Junlong Feng

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Abstract

We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a new theoretical argument to establish consistency without assuming sparsity or the existence of any moments of the error matrix, so that fat-tailed continuous random errors such as Cauchy are allowed. The results are illustrated by simulations.

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Jushan Bai, Junlong Feng. 2019-02-23. Robust Principal Component Analysis with Non-Sparse Errors. https://arxiv.org/abs/1902.08735

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