Principal Components and Principal Fitted Components for Matrix or Array Valued Objects

• Activity Number: 673
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Shanshan Ding*+ and R. Dennis Cook
• Companies: University of Minnesota and University of Minnesota
• Keywords: dimension reduction ; central subspaces ; inverse regression ; principal components ; principal fitted components ; dimension folding

Abstract

We consider principal component analysis and principal fitted component analysis for matrix or array-valued predictors. We call them as dimension folding PCA and dimension folding PFC. The methodology is proposed based on the normal inverse regression model for predictors. For dimension folding PCA, we apply normal models for the inverse regression of the predictors, and for dimension folding PFC, we apply normal inverse models of the predictors on the response, to gain reductive information. For both dimension folding PCA and dimension folding PFC, we consider the cases of isotropic random errors and general random errors. Numerical algorithms for obtaining the maximum likelihood estimators of the sufficient dimension folding central subspaces are derived. We compare the dimension folding PCA and PFC with the traditional PCA and PFC by simulation studies. In addition, the comparison results of these methods with some nonparametric dimension folding methods, such as dimension folding SIR, dimension folding SAVE, are provided.