Anisotropic diffusion on sub-manifolds with application to Earth structure classification

We introduce a method to re-parameterize massive high dimensional data, generated by nonlinear mixing, into its independent physical parameters. Our method enables the identification of the original parameters and their extension to new observations without any knowledge of the true physical model. The suggested approach in this paper is related to spectral independent components analysis (ICA) via the construction of an anisotropic diffusion kernel whose eigenfunctions comprise the independent components. However, we use a novel anisotropic diffusion process, utilizing only a small observed subset Y¯, that approximates the isotropic diffusion on the parametric manifold MX of the full set Y. We employ a Nyström-type extension of the independent components of Y¯ to the independent components of Y, and provide a validation scheme for our algorithm parameters choice. We demonstrate our method on synthetic examples and on real application examples.