LMS and LTS-type Alternatives to Classical Principal Component Analysis

- Journal title : Communications for Statistical Applications and Methods
- Volume 13, Issue 2, 2006, pp.233-241
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2006.13.2.233

Title & Authors

LMS and LTS-type Alternatives to Classical Principal Component Analysis

Huh, Myung-Hoe; Lee, Yong-Goo;

Huh, Myung-Hoe; Lee, Yong-Goo;

Abstract

Classical principal component analysis (PCA) can be formulated as finding the linear subspace that best accommodates multidimensional data points in the sense that the sum of squared residual distances is minimized. As alternatives to such LS (least squares) fitting approach, we produce LMS (least median of squares) and LTS (least trimmed squares)-type PCA by minimizing the median of squared residual distances and the trimmed sum of squares, in a similar fashion to Rousseeuw (1984)'s alternative approaches to LS linear regression. Proposed methods adopt the data-driven optimization algorithm of Croux and Ruiz-Gazen (1996, 2005) that is conceptually simple and computationally practical. Numerical examples are given.

Keywords

Principal component analysis (PCA);Projection pursuit;Least squares (LS);Least median of squares (LMS);Least trimmed squares (LTS);

Language

English

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