Robust principal component analysis via ES-algorithm

Abstract

In this paper, a new method for robust principal component analysis (PCA) is proposed. PCA is a widely used tool for dimension reduction without substantial loss of information. However, the classical PCA is vulnerable to outliers due to its dependence on the empirical covariance matrix. To avoid such weakness, several alternative approaches based on robust scatter matrix were suggested. A popular choice is ROBPCA that combines projection pursuit ideas with robust covariance estimation via variance maximization criterion. Our approach is based on the fact that PCA can be formulated as a regression-type optimization problem, which is the main difference from the previous approaches. The proposed robust PCA is derived by substituting square loss function with a robust penalty function, Huber loss function. A practical algorithm is proposed in order to implement an optimization computation, and furthermore, convergence properties of the algorithm are investigated. Results from a simulation study and a real data example demonstrate the promising empirical properties of the proposed method.