Mapping the dimensionality, density and topology of data: The growing adaptive neural gas

Self-organized maps are commonly applied for tasks of cluster analysis, vector quantization or interpolation. The artificial neural network model introduced in this paper is a hybrid model of the growing neural gas model introduced by Fritzke (Fritzke, in Advances in Neural Information Processing Systems 7, MIT Press, Cambridge MA, 1995) and the adaptive resolution clustering modification for self-organized maps proposed by Firenze (Firenze et al., in International Conference on Artificial Neural Networks, Springer-Verlag, London, 1994). The hybrid model is capable of mapping the distribution, dimensionality and topology of the input data. It has a local performance measure that enables the network to terminate growing in areas of the input space that is mapped by units reaching a performance goal. Therefore the network can accurately map clusters of data appearing on different scales of density. The capabilities of the algorithm are tested using simulated datasets with similar spatial spread but different local density distributions, and a simulated multivariate MR dataset of an anatomical human brain phantom with mild multiple sclerosis lesions. These tests demonstrate the advantages of the model compared to the growing neural gas algorithm when adaptive mapping of areas with low sample density is desirable.