A hybrid batch SOM-NG algorithm

The self-organizing map (SOM) is a suitable algorithm for data visualization but its topological preservation makes the vector quantization non-optimal. This paper aims to improve the lack of quantization precision in the SOM. An energy cost function based on two different kernels is formulated to obtain a batch algorithm. A bivariate normal distribution is assumed to weight the topological preservation versus the vector quantization. The main properties of SOM and neural gas (NG) are combined to obtain a compact and robust learning rule with an efficient computational complexity. The proposed batch SOM-NG was compared to algorithms with procedures and computational complexities that are similar. The results seem to prove that SOM-NG can achieve an acceptable neighborhood preservation obtaining similar values to the SOM with a quantization error almost equal to the one of the NG. In this way, the algorithm has the advantages of SOM and NG for data visualization and vector quantization.