Robust PCA for skewed data and its outlier map

Authors:
Mia Hubert;Peter Rousseeuw;Tim Verdonck
Affiliations:
Department of Mathematics, LSTAT, Katholieke Universiteit Leuven, Belgium;Department of Mathematics and Computer Science, University of Antwerp, Belgium;Department of Mathematics and Computer Science, University of Antwerp, Belgium
Venue:
Computational Statistics & Data Analysis
Year:
2009

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Abstract

The outlier sensitivity of classical principal component analysis (PCA) has spurred the development of robust techniques. Existing robust PCA methods like ROBPCA work best if the non-outlying data have an approximately symmetric distribution. When the original variables are skewed, too many points tend to be flagged as outlying. A robust PCA method is developed which is also suitable for skewed data. To flag the outliers a new outlier map is defined. Its performance is illustrated on real data from economics, engineering, and finance, and confirmed by a simulation study.