SOM IN HILBERT SPACE

The self organization can be performed in an Euclidean space as usually defined or in any metric space which is generalization of previous one. Both approaches have advantages and disadvantages. A novel method of batch SOM learning is designed to yield from the properties of the Hilbert space. This method is able to operate with finite or infinite dimensional patterns from vector space using only their scalar product. The paper is focused on the formulation of objective function and algorithm for its local minimization in a discrete space of partitions. General methodology is demonstrated on pattern sets from a space of functions.