English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a data model in which the data matrix <inline-formula><tex-math notation="LaTeX">$\mathbf {D}\in \mathbb {R}^{N_1 \times N_2}$</tex-math></inline-formula> can be expressed as <inline-formula><tex-math notation="LaTeX">$\mathbf {D}= \mathbf {L}+ \mathbf {S}+ \mathbf {C},$</tex-math></inline-formula> where <inline-formula><tex-math notation="LaTeX">$\mathbf {L}$</tex-math></inline-formula> is a low-rank matrix, <inline-formula><tex-math notation="LaTeX">$\mathbf {S}$</tex-math></inline-formula> is an elementwise sparse matrix, and <inline-formula><tex-math notation="LaTeX">$\mathbf {C}$</tex-math></inline-formula> is a matrix whose nonzero columns are outlying data points. To date, robust principal component analysis (PCA) algorithms have solely considered models with either <inline-formula><tex-math notation="LaTeX">$\mathbf {S}$</tex-math></inline-formula> or <inline-formula><tex-math notation="LaTeX">$\mathbf {C}$</tex-math></inline-formula>, 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 <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-norm minimization can obtain the representation of an inlier in presence of sparse corruptions.

Low-Rank Matrix Recovery With Simultaneous Presence of Outliers and Sparse Corruption