Weight adjusting for a self-organizing artificial neural network in non-Euclidean space

Abstract

Current unsupervised classification using self-organizing competitive learning is based on the minimum Euclidean distance between a prototype neuron and the selected data. Euclidean distance measure does not consider the clustering structure of the data. This approach is not suitable for several classification problems where the geometrical structure and surface of the data space are the main concern. The prototype neurons must flow along the natural curvature of the data space and correctly classify the space. This implies that the distances among the data should be non-Euclidean and measured along the natural structure of the space. The problem studied in this paper concerns the algorithm for measuring the non-Euclidean distance in a data point space, i.e. the surface function is unknown, and moving the prototype neurons along the actual geometrical structure of the data points. Our algorithm successfully classifies the experimental data spaces with various aspects while the unsupervised Euclidean distance classification gives incorrect results.