Projected Principal Component Analysis in Factor Models for Populations of Images

• Activity Number: 604
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Maximillian Chen* and Hongtu Zhu
• Companies: Sandia National Laboratories and The University of North Carolina at Chapel Hill
• Keywords: low rank representation ; additive models ; high-dimensionality ; approximate factor models

Abstract

Much of the research work on high-dimensional analysis has centered on analyzing a population of high-dimensional vectors. However, not as much work has been done on analyzing a population of high-dimensional matrices. Fan et al (2014) introduce the Projected Principal Component Analysis (Projected-PCA) method, which performs factor analysis on a population of high-dimensional vectors and projects the data matrix into a given linear space of known covariates before performing the principal component analysis. Ahn et al (2013) introduce the sparse reduced rank (SRR) framework for selection of sparsity level and model rank for a population of functional neuroimaging data. We propose a method for performing Projected-PCA over a population of matrix images, which extends the Projected-PCA method to the SRR framework. We apply smoothness and sparseness penalties to determine the model rank and the dimensions of the basis space over known covariates, and we discuss hypothesis testing procedures. Practical implementation of the methods will be discussed.