Self-organization on a Sphere with Application to Topological Ordering of Chinese Characters

摘要

We consider a case of self-organization in which a relatively small number TV of data points is mapped on a larger number M of nodes. This is a reverse situation to a typical clustering problem when a node represents a center of the cluster of data points. In our case the objective is to have a Gaussian-like distribution of weights over nodes in the neighbourhood of the winner for a given stimulus. The fact that M ＞ N creates some problem with using learning schemes related to Gaussian Mixture Models. We also show how the objects, Chinese characters in our case, can be topologically ordered on a surface of a 3D sphere. A Chinese character is represented by an angular integral of the Radon Transform (aniRT) which is an RTS-invariant 1-D signature function of an image.