Shun-ichi Amari

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A new on-line learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of the sources. The Gram-Charlier expansion instead of the(More)
In this book, we describe various approaches, methods and techniques to blind and semi-blind signal processing, especially principal and independent component analysis, blind source separation, blind source extraction, multichannel blind deconvolution and equalization of source signals when the measured sensor signals are contaminated by additive noise.(More)
An exponential family or mixture family of probability distributions has a natural hierarchical structure. This paper gives an “orthogonal” decomposition of such a system based on information geometry. A typical example is the decomposition of stochastic dependency among a number of random variables. In general, they have a complex structure of(More)
We propose a method of modifying a kernel function to improve the performance of a support vector machine classiier. This is based on the Riemannian geometrical structure induced by the kernel function. The idea is to enlarge the spatial resolution around the separating boundary surface by a conformal mapping such that the separability between classes is(More)
The problem of model selection, or determination of the number of hidden units, can be approached statistically, by generalizing Akaike's information criterion (AIC) to be applicable to unfaithful (i.e., unrealizable) models with general loss criteria including regularization terms. The relation between the training error and the generalization error is(More)
In this paper we discus a wide class of loss (cost) functions for non-negative matrix factorization (NMF) and derive several novel algorithms with improved efficiency and robustness to noise and outliers. We review several approaches which allow us to obtain generalized forms of multiplicative NMF algorithms and unify some existing algorithms. We give also(More)
The dynamic behavior of randomly connected analog neuron-like elements that process pulse-frequency modulated signals is investigated from the macroscopic point of view. By extracting two statistical parameters, the macroscopic state equations are derived in terms of these parameters under some hypotheses on the stochastics of microscopic states. It is(More)