A0190
Title: On the efficiency-loss free ordering-robustness of product-PCA
Authors: Hung Hung - National Taiwan University (Taiwan) [presenting]
Su-Yun Huang - Academia Sinica (Taiwan)
Abstract: The robustness of the eigenvalue ordering, an important issue, is studied when estimating the leading eigen-subspace by principal component analysis (PCA). Previously, cross-data-matrix PCA (CDM-PCA) was proposed and shown to have smaller bias than PCA in estimating eigenvalues. While CDM-PCA has the potential to achieve a better estimation of the leading eigen-subspace than the usual PCA, its robustness is not well recognized. First, a more stable variant of CDM-PCA, is developed, called product-PCA (PPCA), that provides a more convenient formulation for theoretical investigation. Secondly, it is proved that, in the presence of outliers, PPCA is more robust than PCA in maintaining the correct ordering of leading eigenvalues. The robustness gain in PPCA comes from the random data partition, and it does not rely on a data down-weighting scheme as most robust statistical methods do. This enables us to establish the surprising finding that when there are no outliers, PPCA and PCA share the same asymptotic distribution. That is the robustness gain of PPCA in estimating the leading eigen-subspace has no efficiency loss in comparison with PCA. Simulation studies and a face data example are presented to show the merits of PPCA. In conclusion, PPCA has a good potential to replace the role of the usual PCA in real applications whether outliers are present or not.
