Some further evidence about magnification and shape in neural gas

Neural gas (NG) is a robust vector quantization algorithm for which a descriptive mathematical model is known. According to this model, the output configuration produced by the NG algorithm samples the input data distribution with a density that follows a power law with a magnification factor that depends on data dimensionality only. The effects of shape in the input data distribution on the NG behavior, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The results of the experimental work described here show that the effects of shape are indeed relevant; more specifically, experiments reveal that shape can induce richer and more complex NG behaviors than those predicted by the power law alone. Although a more comprehensive analytical model remains to be defined, the evidence collected in these experiments suggests that these specific NG behaviors have an interesting potential for detecting complex shapes in noisy datasets.