Robust CUR Decomposition: Theory and Imaging Applications Article Swipe

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HanQin Cai , Keaton Hamm , Longxiu Huang , Deanna Needell ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2101.05231

This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where $\mathbf{L}$ is low-rank and $\mathbf{S}$ contains sparse outliers. These methods yield interpretable factorizations at low computational cost, and provide new CUR decompositions that are robust to sparse outliers, in contrast to previous methods. We consider two key imaging applications of Robust PCA: video foreground-background separation and face modeling. This paper examines the qualitative behavior of our Robust CUR decompositions on the benchmark videos and face datasets, and find that our method works as well as standard Robust PCA while being significantly faster. Additionally, we consider hybrid randomized and deterministic sampling methods which produce a compact CUR decomposition of a given matrix, and apply this to video sequences to produce canonical frames thereof.

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Benchmark (Surveying)

Computer Science

Lock And Key

Principal Component Analysis

Algorithm

Artificial Intelligence

Concepts

Outlier Decomposition Robust principal component analysis Benchmark (surveying) Matrix decomposition Computer science Rank (graph theory) Key (lock) Matrix (chemical analysis) Principal component analysis Algorithm Artificial intelligence Mathematics Pattern recognition (psychology) Combinatorics Materials science Eigenvalues and eigenvectors Biology Computer security Quantum mechanics Geography Ecology Composite material Geodesy Physics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2101.05231
PDF: https://arxiv.org/pdf/2101.05231
OA Status: green
Cited By: 9
References: 38
Related Works: 10
OpenAlex ID: https://openalex.org/W3118450185

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DOI: https://doi.org/10.48550/arxiv.2101.05231

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Title: Robust CUR Decomposition: Theory and Imaging Applications

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Type: preprint

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Language: en

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Publication year: 2021

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Publication date: 2021-01-05

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Authors: HanQin Cai, Keaton Hamm, Longxiu Huang, Deanna Needell

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Landing page: https://arxiv.org/abs/2101.05231

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Concepts: Outlier, Decomposition, Robust principal component analysis, Benchmark (surveying), Matrix decomposition, Computer science, Rank (graph theory), Key (lock), Matrix (chemical analysis), Principal component analysis, Algorithm, Artificial intelligence, Mathematics, Pattern recognition (psychology), Combinatorics, Materials science, Eigenvalues and eigenvectors, Biology, Computer security, Quantum mechanics, Geography, Ecology, Composite material, Geodesy, Physics

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Cited by: 9

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Citations by year (recent): 2025: 1, 2024: 1, 2023: 2, 2021: 5

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abstract_inverted_index.sparse	36, 56
abstract_inverted_index.videos	92
abstract_inverted_index.compact	124
abstract_inverted_index.faster.	111
abstract_inverted_index.imaging	67
abstract_inverted_index.matrix,	130
abstract_inverted_index.methods	39, 120
abstract_inverted_index.produce	19, 122, 138
abstract_inverted_index.provide	48
abstract_inverted_index.version	22
abstract_inverted_index.behavior	83
abstract_inverted_index.consider	64, 114
abstract_inverted_index.contains	35
abstract_inverted_index.contrast	59
abstract_inverted_index.examines	80
abstract_inverted_index.low-rank	32
abstract_inverted_index.matrices	27
abstract_inverted_index.methods.	62
abstract_inverted_index.previous	61
abstract_inverted_index.sampling	119
abstract_inverted_index.standard	105
abstract_inverted_index.thereof.	15, 141
abstract_inverted_index.benchmark	91
abstract_inverted_index.canonical	139
abstract_inverted_index.considers	2
abstract_inverted_index.datasets,	95
abstract_inverted_index.framework	12
abstract_inverted_index.modeling.	77
abstract_inverted_index.outliers,	57
abstract_inverted_index.outliers.	37
abstract_inverted_index.sequences	136
abstract_inverted_index.algorithms	18
abstract_inverted_index.column-row	24
abstract_inverted_index.randomized	116
abstract_inverted_index.separation	74
abstract_inverted_index.qualitative	82
abstract_inverted_index.$\mathbf{L}$	30
abstract_inverted_index.$\mathbf{S}$	34
abstract_inverted_index.applications	14, 68
abstract_inverted_index.Additionally,	112
abstract_inverted_index.computational	45
abstract_inverted_index.decomposition	11, 126
abstract_inverted_index.deterministic	118
abstract_inverted_index.interpretable	41
abstract_inverted_index.significantly	110
abstract_inverted_index.decompositions	51, 88
abstract_inverted_index.factorizations	25, 42
abstract_inverted_index.foreground-background	73
abstract_inverted_index.$\mathbf{D}=\mathbf{L}+\mathbf{S}$	28
cited_by_percentile_year.max	98
cited_by_percentile_year.min	90
countries_distinct_count	0
institutions_distinct_count	4
citation_normalized_percentile.value	0.77887071
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False