Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Composite algorithm for adaptive mesh construction based on self-organizing maps
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
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The usual ’Kohonen‘ algorithm uses samples of points in a domainto develop a topological correspondence between a grid of ’neurons‘and a continuous domain. ’Topological‘ means that near points are mapped to near points. However, for many applications there are additionalconstraints, which are given by sets of measure zero,which are not preserved by this method, because of insufficient sampling. In particular,boundary points do not typically map to boundary points because in generalthe likelihood of a sample point from a two-dimensional domain falling on the boundary is typically zero for continuous data,and extremely small for numerical data. A specific application, (assigning meshes for the finite element method),was recently solved by interweaving a two-dimensional Kohonen mappingon the entire grid with a one-dimensional Kohonen mapping on the boundary.While the precise method of interweaving was heuristic, the underlying rationale seems widely applicable.This general method is problemindependent and suggests a direct generalization to higher dimensionsas well.