On Multilinear Principal Component Analysis of Order-Two Tensors

• Activity Number: 432
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): I-Ping Tu*+ and Hung Hung and Su-Yun Huang and Peishien Wu
• Companies: Academia Sinica and Institute of Epidemiology and Preventive Medicine, National Taiwan University and Institute of Statistical Science, Academia Sinica and Institute of Statistical Science, Academia Sinica
• Keywords: Dimension reduction ; Image reconstruction ; Tensor ; Principal component analysis

Abstract

Principal component analysis is a commonly used tool for dimension reduction in analyzing high dimensional data. Multilinear principal component analysis aims to serve a similar function for analyzing tensor structure data, and has been shown effective in reducing dimensionality both through real data analyses and through simulations. In this paper, we investigate statistical properties of multilinear principal component analysis and provide explanations for its advantages. Asymptotic theory of order-two multilinear principal component analysis, including asymptotic efficiency and asymptotic distributions of principal components, associated projections, and the explained variance, is developed. A test of dimensionality is also proposed. Finally, multilinear principal component analysis is shown to improve conventional principal component analysis in analyzing the Olivetti Faces data set, which is achieved by extracting a more modularly-oriented basis set in reconstructing the test faces.