Mathematics – Statistics Theory
Scientific paper
2011-04-28
Mathematics
Statistics Theory
33 pages, 2 tables, 7 figures
Scientific paper
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor structure data. MPCA and other tensor decomposition methods have been proved effective to reduce the dimensions for both real data analyses and simulation studies (Ye, 2005; Lu, Plataniotis and Venetsanopoulos, 2008; Kolda and Bader, 2009; Li, Kim and Altman, 2010). In this paper, we investigate MPCA's statistical properties and provide explanations for its advantages. Conventional PCA, vectorizing the tensor data, may lead to inefficient and unstable prediction due to its extremely large dimensionality. On the other hand, MPCA, trying to preserve the data structure, searches for low-dimensional multilinear projections and decreases the dimensionality efficiently. The asymptotic theories for order-two MPCA, including asymptotic distributions for principal components, associated projections and the explained variance, are developed. Finally, MPCA is shown to improve conventional PCA on analyzing the {\sf Olivetti Faces} data set, by constructing more module oriented basis in reconstructing the test faces.
Huang Su-Yun
Hung Hung
Tu I-Ping
Wu Pei-Shien
No associations
LandOfFree
On Multilinear Principal Component Analysis of Order-Two Tensors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Multilinear Principal Component Analysis of Order-Two Tensors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Multilinear Principal Component Analysis of Order-Two Tensors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-448835