Nonlinear Geometric Ica

We present a new algorithm for nonlinear blind source separation, which is based on the geometry of the mixture space. This space is decomposed in a set of concentric rings, in which we perform ordinary linear ICA after central transformation; we show that this transformation can be left out if we use linear geometric ICA. In any case, we get a set of images of ring points under the original mixing mapping. Putting those together we can reconstruct the mixing mapping. Indeed, this approach contains linear ICA and postnonlinear ICA after whitening. The paper finishes with various examples on toy and speech data.