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A stratification and manifold learning approach for analyzing High Angular Resolution Diffusion Imaging (HARDI) data is introduced in this paper. HARDI data provides high- dimensional signals measuring the complex microstructure of biological tissues, such as the cerebral white matter. We show that these high-dimensional spaces may be understood as unions of manifolds of varying dimensions/complexity and densities. With such analysis, we use clustering to characterize the structural complexity of the white matter. We briefly present the underlying framework and numerical experiments illustrating this original and promising approach.