Orthogonal series density estimation and the kernel eigenvalue problem
Neural Computation
Optimal kernel selection in Kernel Fisher discriminant analysis
ICML '06 Proceedings of the 23rd international conference on Machine learning
Diffeomorphic Matching of Diffusion Tensor Images
CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
Journal of Mathematical Imaging and Vision
Biomarkers for identifying first-episode schizophrenia patients using diffusion weighted imaging
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
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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 R6, 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.