Topology preserving using harmonic competitive neural networks

Abstract

Topology preservation is mainly used to analyze the structure of an input distribution. In some implementations, it refers to a data visualization process by means of which high-dimensional input data can be mapped onto a lower-dimensional space where the spatial features of the original input data can be visually revealed. In this paper, we propose a powerful topology-preserving method based on a self-creating model called the harmonic competitive neural network (HCNN). The HCNN is initialized as a triangular structure (i.e. three nodes connected to each other), as in the growing cell structure (GCS) of B. Fritzke (1994). In order to approximate the input distribution in a self-organizing manner, the training parameters are data-driven and the network size does not need to be pre-specified. Our goal is to map the topological structure of input data with less distortion error and lower computational cost in comparison with other networks, such as self-organizing feature maps (SOFMs) or topology-representing networks (TRNs).