Some Further Evidence about Magnification and Shape in Neural Gas

TL;DR

This paper investigates how the shape of data distributions influences neural gas behavior, revealing complex effects beyond the traditional power law model and highlighting its potential for detecting intricate shapes in noisy data.

Contribution

It provides experimental evidence that data shape affects neural gas performance, extending understanding beyond the existing power law model.

Findings

Shape influences neural gas behavior significantly.

Complex behaviors induced by shape are observed.

Neural gas shows potential for detecting complex shapes.

Abstract

Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on data dimensionality only. The effects of shape in the input data distribution, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The experimental work described here shows that shape is indeed relevant in determining the overall NG behavior; in particular, some experiments reveal richer and complex behaviors induced by shape that cannot be explained by the power law alone. Although a more comprehensive analytical model remains to be defined, the evidence collected in these experiments suggests that the NG algorithm has an interesting potential for detecting complex shapes in noisy datasets.