Robust Principal Component Analysis

Abstract

In multivariate analysis, principal component analysis is a widely popular method which is used in many different fields. Though it has been extensively shown to work well when data follows multivariate normality, classical PCA suffers when data is heavy-tailed. Using PCA with the assumption that the data follows a stable distribution, we will show through simulations that a new method is better. We show the modified PCA can be used for heavy-tailed data and that we can more accurately estimate the correct number of components compared to classical PCA and more accurately identify the subspace spanned by the important components.