Fast sequential implementation of "neural-gas" network for vector quantization

Although the "neural-gas" network proposed by Martinetz et al. in 1993 has been proven for its optimality in vector quantizer design and has been demonstrated to have good performance in time-series prediction, its high computational complexity (NlogN) makes it a slow sequential algorithm. We suggest two ideas to speedup its sequential realization: (1) using a truncated exponential function as its neighborhood function and (2) applying a new extension of the partial distance elimination method (PDE). This fast realization is compared with the original version of the neural-gas network for codebook design in image vector quantization. The comparison indicates that a speedup of five times is possible, while the quality of the resulting codebook is almost the same as that of the straightforward realization.