Stochastic on-line algorithm versus batch algorithm for quantization and self organizing maps

The Kohonen algorithm (SOM) was originally designed as a stochastic algorithm which works in an on-line way and which was designed to model some adaptative features of the human brain. In fact it is nowadays extensively used for data mining, data visualization, and exploratory data analysis. Some users are tempted to use the batch version of the Kohonen algorithm since it is a deterministic algorithm which can be convenient if one needs to get reproducible results and which can go faster in some cases. In this paper, we try to elucidate the mathematical nature of this batch variant and give some elements of comparison of both algorithms. Then we compare both versions on a real data set.