Cauchy robust principal component analysis with applications to high-dimensional data sets

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate Gaussian likelihood. As a consequence of the implied Gaussian f...

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Bibliographic Details
Published in:Statistics and computing 2024-02, Vol.34 (1), Article 26
Main Authors: Fayomi, Aisha, Pantazis, Yannis, Tsagris, Michail, Wood, Andrew T. A.
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Computer Science
Influence functions
Multivariate analysis
Original Paper
Outliers (statistics)
Principal components analysis
Probability and Statistics in Computer Science
Public domain
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
Citations: Items that this one cites
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Summary:Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate Gaussian likelihood. As a consequence of the implied Gaussian formulation, the principal components are not robust to outliers. In this paper, we propose a modified formulation, based on the use of a multivariate Cauchy likelihood instead of the Gaussian likelihood, which has the effect of robustifying the principal components. We present an algorithm to compute these robustified principal components. We additionally derive the relevant influence function of the first component and examine its theoretical properties. Simulation experiments on high-dimensional datasets demonstrate that the estimated principal components based on the Cauchy likelihood typically outperform, or are on a par with, existing robust PCA techniques. Moreover, the Cauchy PCA algorithm we have used has much lower computational cost in very high dimensional settings than the other public domain robust PCA methods we consider.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-023-10328-x