Kernel-based manifold learning for statistical analysis of diffusion tensor images

Diffusion tensor imaging (DTI) is an important modality to study white matter structure in brain images and voxel-based group-wise statistical analysis of DTI is an integral component in most biomedical applications of DTI. Voxel-based DTI analysis should ideally satisfy two desiderata: (1) it should obtain a good characterization of the statistical distribution of the tensors under consideration at a given voxel, which typically lie on a non-linear submanifold of R-6, and (2) it should find an optimal way to identify statistical differences between two groups of tensor measurements, e.g., as in comparative studies between normal and diseased populations. In this paper, extending previous work on the application of manifold learning techniques to DTI, we shall present a kernel-based approach to voxel-wise statistical analysis of DTI data that satisfies both these desiderata. Using both simulated and real data, we shall show that kernel principal component analysis (kPCA) can effectively learn the probability density of the tensors under consideration and that kernel Fisher discriminant analysis (kFDA) can find good features that can optimally discriminate between groups. We shall also present results from an application of kFDA to a DTI dataset obtained as part of a clinical study of schizophrenia.