Vector quantization by optimal neural gas

Many vector quantization algorithms have been designed to minimize the reconstruction error of the data representation. The additional requirement of topology preservation in self-organizing maps conflicts this goal but can be alleviated by suitable modifications. In the present contribution we demonstrate that the neural gas algorithm allows for vector quantization with a theoretically optimal reconstruction error over an extended range of parameters. Moreover, by a similar scheme as previously applied to self-organizing maps it is possible to modify the neural gas algorithm such as to meet optimality criteria other than the reconstruction error in a way which is exact for arbitrary dimensionality of the data.