Brain Mapping Data: Classification, Principal Components and Multidimensional Scaling

Brain mapping data consists of 3D images of brain function (blood flow or blood oxygenation dependent response), or brain anatomy (MRI images), repeated under different experimental conditions and over different subjects. We can regard the image values, sampled at up to 500,000 voxels, as a very high dimensional multivariate observation, but a better approach is to model them as a continuous function or random field. The result of the statistical analysis is an image of test statistics, and our main interest is how to deal with them. We use a topological quantity, the Euler characteristic of the excursion set of a random field, as a tool to test for localised changes. The data is highly non-isotropic, that is, the effective smoothness is not constant across the image, so the usual random field theory does not apply. We propose a solution that warps the data to isotropy using local multidimensional scaling. Recent theoretical work has shown that the subsequent corrections to the random field theory can be done without actually doing the warping (Taylor and Adler, 2002). We shall apply these methods to a set of 151 brain images from the Human Brain Mapping data base.