Robust principal component analysis based on pairwise correlation estimators

Abstract

Principal component analysis tries to explain and simplify the structure of multivariate data. For standardized variables, these principal components correspond to the eigenvectors of their correlation matrix. To obtain a robust principal components analysis, we estimate this correlation matrix componentwise by using robust pairwise correlation estimates. We show that the approach based on pairwise correlation estimators does not need a majority of outlier-free observations which becomes very useful for high dimensional problems. We further demonstrate that the "bivariate trimming" method especially works well in this setting. © Springer-Verlag Berlin Heidelberg 2010.