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Activity Number: 335
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #306088
Title: Optimal Dimension Reduction and Hypothesis Testing for Populations of Images
Author(s): Maximillian Chen*+ and Martin Wells
Companies: Cornell University and Cornell University
Address: 210 Lake Street, Ithaca, NY, 14850, United States
Keywords: statistical modeling ; high-dimensional data ; hypothesis testing ; dimension reduction

The population value decomposition (PVD) by Crainiceanu et al (2011) is a method for dimension reduction of a population of massive images. Images are decomposed into a product of two orthogonal matrices with population-specific features and one matrix with subject-specific features. The problems of finding the optimal row and column dimensions of reduction and performing inference on the reduced images remain unsolved. Incorporating PVD as a multivariate regression problem, we introduce an iterative method for finding the optimal dimensions of reduction that is based on the Rank Selection Criterion by Bunea et al (2011) and the low-rank approximation and optimization methods of Manton et al (2003). In addition, we introduce a likelihood-ratio test for the two-population problem. The orthogonality constraints on the population-specific images need to be maintained for identifiability reasons. Therefore, construction of our likelihood-ratio test involves quasi-Newton methods for objective functions defined on Grassmannians. Simulation studies will be used to illustrate these methods.

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