Robust Principal Component Analysis in Multivariate Applications

Principal component analysis (PCA) is one of the multivariate methods that aims to construct components, each of which contains a maximal amount of variation from the data unexplained by the other components. Classical PCA (CPCA) is based on the classical covariance, which is easily affected by outliers. Additionally, the outliers may distort the PCA result. Robust statistics is one of the methods to overcome the outliers. Therefore, in this study, an alternative technique for robust principal component analysis (RPCA) is presented. Index Set Equality (ISE) is used as a robust estimator to robustify the CPCA and hence produce robust PCA (RPCA). The Hawkins-Bradu Kass dataset is used to illustrate the robustness of RPCA towards outliers compared to CPCA. The score plot, diagnostic plot, and performance measures are used to evaluate and illustrate the robustness of the RPCA. From the plots and performance measures, RPCA successfully identifies all outliers and is unaffected by masking and swamping effects. However, CPCA can only detect 0.2857 outliers, has 0.7143 masking effects, but does not have swamping effects. This study shows that RPCA, by using ISE as the robust estimator is a promising approach.