Shun-ichi Amari

TL;DR: In this paper, the authors used information geometry to calculate the natural gradients in the parameter space of perceptrons, the space of matrices (for blind source separation), and the spaces of linear dynamical systems for blind source deconvolution, and proved that Fisher efficient online learning has asymptotically the same performance as the optimal batch estimation of parameters.

TL;DR: A new on-line learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals and has an equivariant property and is easily implemented on a neural network like model.

TL;DR: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF), including NMFs various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD).

TL;DR: The dynamics of pattern formation is studied for lateral-inhibition type homogeneous neural fields with general connections and it is proved that there are five types of pattern dynamics.