Self-organizing topological tree

The self-organizing maps (SOM) introduced by Kohonen implemented two important operations: vector quantization (VQ) and a topology-preserving mapping. In this paper, a tree structured SOM algorithm named self-organizing topological tree (SOTT) is proposed. Unlike the conventional tree structured SOMs as stated in T. Kohonen (2001), P. Koikkalainnen and E. Oja (1990) and P. Koikkalainnen (1994), every layer of the proposed SOTT is organized simultaneously instead of layer by layer. A reduction of computational complexity from O(N) to O(logN) is achieved by the tree structured search in both the training phase and the test phase. Furthermore, such topological tree that maintains both intra-layer and inter-layer topologies during and after learning can be seen as endowing the SOM topological map with the progressive decoding and multi-resolution capabilities.