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Self-organizing homotopy network

Furukawa, Tetsuo

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In this paper, we propose a conceptual learning algorithm called the 'self-organizing homotopy (SOH)' together with an implementation thereof. As in the case of the SOM, our SOH organizes a homotopy in a self-organizing manner by giving a set of data episodes. Thus it is an extension of the SOM, moving from a 'map' to a 'homotopy'. From a geometrical viewpoint, the SOH represents a set of (i.e. multiple) data distributions by a fiber bundle, whereas the SOM represents a single data distribution by a manifold. One of the solutions to the SOH is SOM², in which every reference vector unit of the conventional SOM is itself replaced by an SOM. Consequently SOM² has the ability to represent a fiber bundle, i.e. a product manifold, by using a product space of SOM x SOM. It is expected that SOHs will play important roles in the fields of pattern recognition, adaptive functions, context understanding, and others, in which nonlinear manifolds and the homotopy play crucial roles.

Keywords: homotopy, fiber bundle, SOM², mnSOM
Institution: Faculty of Technology, Research Groups in Informatics
DDC classification: Data processing, computer science, computer systems

Suggested Citation:
Furukawa, Tetsuo  (2007)  Self-organizing homotopy network.

URL: http://biecoll.ub.uni-bielefeld.de/volltexte/2007/145

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