A Unified Framework of Robust PCA: Use of Robust Unit Approach

Abstract

In this paper, we propose a new framework of robust PCA for improving the robustness and for reflecting various outlier types as well as skewed data. This framework is composed of two concepts: robust unit that is induced by a combination of any PCA procedure and a restriction function as an outlier filter and two-stage strategy that divides and conquers outliers. As a practical implementation of the proposed framework, we develop a robust PCA procedure, termed robust pair PCA (RP-PCA) by coupling a t-distribution-based probabilistic PCA (T-PCA) with our framework. Moreover, for missing data, we suggest a new procedure for handling missing values that fully exploits EM algorithm of T-PCA under the robust unit. Empirical performance of the proposed method is evaluated through numerical studies including simulation study and real data analysis, which demonstrates promising results of the proposed robust method.