Robust principal component analysis for generalized multi-view models

Frank Nussbaum, Joachim Giesen
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:686-695, 2021.

Abstract

It has long been known that principal component analysis (PCA) is not robust with respect to gross data corruption. This has been addressed by robust principal component analysis (RPCA). The first computationally tractable definition of RPCA decomposes a data matrix into a low-rank and a sparse component. The low-rank component represents the principal components, while the sparse component accounts for the data corruption. Previous works consider the corruption of individual entries or whole columns of the data matrix. In contrast, we consider a more general form of data corruption that affects groups of measurements. We show that the decomposition approach remains computationally tractable and allows the exact recovery of the decomposition when only the corrupted data matrix is given. Experiments on synthetic data corroborate our theoretical findings, and experiments on several real-world datasets from different domains demonstrate the wide applicability of our generalized approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-nussbaum21a, title = {Robust principal component analysis for generalized multi-view models}, author = {Nussbaum, Frank and Giesen, Joachim}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {686--695}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/nussbaum21a/nussbaum21a.pdf}, url = {https://proceedings.mlr.press/v161/nussbaum21a.html}, abstract = {It has long been known that principal component analysis (PCA) is not robust with respect to gross data corruption. This has been addressed by robust principal component analysis (RPCA). The first computationally tractable definition of RPCA decomposes a data matrix into a low-rank and a sparse component. The low-rank component represents the principal components, while the sparse component accounts for the data corruption. Previous works consider the corruption of individual entries or whole columns of the data matrix. In contrast, we consider a more general form of data corruption that affects groups of measurements. We show that the decomposition approach remains computationally tractable and allows the exact recovery of the decomposition when only the corrupted data matrix is given. Experiments on synthetic data corroborate our theoretical findings, and experiments on several real-world datasets from different domains demonstrate the wide applicability of our generalized approach.} }
Endnote
%0 Conference Paper %T Robust principal component analysis for generalized multi-view models %A Frank Nussbaum %A Joachim Giesen %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-nussbaum21a %I PMLR %P 686--695 %U https://proceedings.mlr.press/v161/nussbaum21a.html %V 161 %X It has long been known that principal component analysis (PCA) is not robust with respect to gross data corruption. This has been addressed by robust principal component analysis (RPCA). The first computationally tractable definition of RPCA decomposes a data matrix into a low-rank and a sparse component. The low-rank component represents the principal components, while the sparse component accounts for the data corruption. Previous works consider the corruption of individual entries or whole columns of the data matrix. In contrast, we consider a more general form of data corruption that affects groups of measurements. We show that the decomposition approach remains computationally tractable and allows the exact recovery of the decomposition when only the corrupted data matrix is given. Experiments on synthetic data corroborate our theoretical findings, and experiments on several real-world datasets from different domains demonstrate the wide applicability of our generalized approach.
APA
Nussbaum, F. & Giesen, J.. (2021). Robust principal component analysis for generalized multi-view models. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:686-695 Available from https://proceedings.mlr.press/v161/nussbaum21a.html.

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