Non Linear Independent Component Analysis with Diffusion Maps
نویسندگان
چکیده
We introduce intrinsic, nonlinearly invariant, parameterizations of empirical data, generated by a nonlinear transformation of independent variables. This is achieved through anisotropic diffusion kernels on observable data manifolds that approximate a Laplacian on the inaccessible independent variable domain. The key idea is a symmetrized second order approximation of the unknown distances in the independent variable domain, using the metric distortion induced by the Jacobian of the unknown mapping from variables to data. This distortion is estimated using local principal component analysis. We obtain the non linear independent components of stochastic processes and indicate other possible applications.
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