Kernel Feature Spaces and Nonlinear Blind Souce Separation

In kernel based learning the data is mapped to a kernel feature space of a dimension that corresponds to the number of training data points. In practice, however, the data forms a smaller submanifold in feature space, a fact that has been used e.g. by reduced set techniques for SVMs. We propose a new mathematical construction that permits to adapt to the intrinsic dimension and to find an orthonormal basis of this submanifold. In doing so, computations get much simpler and more important our theoretical framework allows to derive elegant kernelized blind source separation (BSS) algorithms for arbitrary invertible nonlinear mixings. Experiments demonstrate the good performance and high computational efficiency of our kTDSEP algorithm for the problem of nonlinear BSS.