Population Value Decomposition, a Framework for the Analysis of Image Populations

Images, often stored in multidimensional arrays, are fast becoming ubiquitous in medical and public health research. Analyzing populations of images is a statistical problem that raises a host of daunting challenges. The most significant challenge is the massive size of the datasets incorporating images recorded for hundreds or thousands of subjects at multiple visits. We introduce the population value decomposition (PVD), a general method for simultaneous dimensionality reduction of large populations of massive images. We show how PVD can be seamlessly incorporated into statistical modeling, leading to a new, transparent, and rapid inferential framework. Our PVD methodology was motivated by and applied to the Sleep Heart Health Study, the largest community-based cohort study of sleep containing more than 85 billion observations on thousands of subjects at two visits. This article has supplementary material online.