Some Further Evidence about Magnification and Shape in Neural Gas

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

Some Theoretical Aspects of the Neural Gas Vector Quantizer

Villmann T, Hammer B, Biehl M. Some theoretical aspects of the neural gas vector quantizer. In: Biehl M, Hammer B, Verleysen M, Villmann T, eds. Similarity Based Clustering. Lecture Notes Artificial Intelligence, 5400. Berlin, Heidelberg: Springer; 2009: 23-34