This paper introduces a novel framework for performing machine learning onlongitudinal neuroimaging datasets. These datasets are characterized by theirsize, particularly their width (millions of features per data input). Specifically, we address the problem of detecting subtle, short-term changes inneural structure that are indicative of cognitive change and correlate withrisk factors for Alzheimer's disease. We introduce a new spatially-sensitivekernel that allows us to reason about individuals, as opposed to populations. In doing so, this paper presents the first evidence demonstrating that verysmall changes in white matter structure over a two year period can predictchange in cognitive function in healthy adults.

This paper explores a new measure of similarity between point sets in arbitrary metric spaces. The measure is based on the spatial overlap of the “shapes” and “densities” of these point sets. It is applicable in any domain where point sets are a natural representation for data. Specifically, we show examples of its use in natural language processing, object recognition in images and point set classification. We provide a geometric interpretation of this measure and show that it is well-motivated, intuitive, parameter-free, and straightforward to use. We further demonstrate that it is computationally tractable and applicable to both supervised and unsupervised learning problems.