Cauchy robust principal components analysis with applications to high dimensional datasets

Andrew Wood; Aisha Fayomi; Yannis Pantazis; Michail Tsagris

Cauchy robust principal components analysis with applications to high dimensional datasets

Andrew Wood, Aisha Fayomi, Yannis Pantazis, Michail Tsagris

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we propose a modified formulation of the principal components analysis, 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.

Original language	English
Article number	26
Number of pages	14
Journal	Statistics and Computing
Volume	34
Publication status	Published - 2 Nov 2023

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https://link.springer.com/article/10.1007/s11222-023-10328-x

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title = "Cauchy robust principal components analysis with applications to high dimensional datasets",

abstract = "In this paper, we propose a modified formulation of the principal components analysis, 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.",

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AB - In this paper, we propose a modified formulation of the principal components analysis, 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.

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JO - Statistics and Computing

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Cauchy robust principal components analysis with applications to high dimensional datasets

Abstract

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