Self-organizing homotopy networks: Comparisons among modular network SOM, SOM of SOMs and parametric bias method

The purpose of this paper is to compare self-organizing homotopy networks. Homotopy is a mathematical concept representing a continuous change between maps or functions, and it is useful in describing a theoretical aspect of the adaptability of neural networks. For this purpose, we examined three neural network architectures: the modular network self-organizing map (mnSOM), the SOM of SOMs (SOM2), and the neural network with parametric bias units (NNPB). To make comparisons, these three architectures were trained to represent a set of polynomial functions under two different conditions. The results suggest that the SOM of SOMs is the best architecture for representing homotopy naturally.