The infomin principle for ICA and topographic mappings

Authors:
Yoshitatsu Matsuda;Kazunori Yamaguchi
Affiliations:
Kazunori Yamaguchi Laboratory, Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan;Kazunori Yamaguchi Laboratory, Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
Venue:
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Year:
2006

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Abstract

It has been well known that edge filters in the visual system can be generated by the InfoMax principle. In this paper, the “InfoMin” principle is proposed, which asserts that the information through some neighboring signals on a two-dimensional mapping must be minimized. It is shown that the standard Comon’s ICA can be derived from the combination of the InfoMax principle for the whole signals and the InfoMin one for each signal under a linear model with sufficiently large noise. It is also shown that the InfoMin principle for the signals within neighboring areas can generate a topographic mapping in the same way as in topographic ICA.