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Cauchy Robust Principal Component Analysis with Applications to High-Dimensional Data Sets

Author

Listed:
  • Aisha Fayomi
  • Yannis Pantazis
  • Michail Tsagris
  • Andrew Wood

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.

Suggested Citation

  • Aisha Fayomi & Yannis Pantazis & Michail Tsagris & Andrew Wood, 2023. "Cauchy Robust Principal Component Analysis with Applications to High-Dimensional Data Sets," Working Papers 2304, University of Crete, Department of Economics.
    • Handle: RePEc:crt:wpaper:2304
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    File URL: https://economics.soc.uoc.gr/wpa/docs/2304.pdf
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    More about this item

    Keywords

    Principal component analysis; robust; Cauchy log-likelihood; high-dimensional data;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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