Advantages and drawbacks of the Batch Kohonen algorithm Jean-Claude Fort 1 , Patrick Letremy 2 , Marie Cottrell 2 1 Institut Elie Cartan et SAMOS-MATISSE Université Nancy 1, F-54506 Vandoeuvre-Lès-Nancy, France fortjc@iecn.u-nancy.fr 2 Université Paris I, SAMOS-MATISSE, UMR CNRS 8595 90 rue de Tolbiac, F-75634 Paris Cedex 13, France pley,cottrell@univ-paris1.fr Abstract : The Kohonen algorithm (SOM) was originally defined as a stochastic algorithm which works in an on-line way and which was designed to model some plastic 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 (KBATCH) since it is a deterministic algorithm which can go faster in some cases. After [7], which tried to elucidate the mathematical nature of the Batch variant, in this paper, we give some elements of comparison for both algorithms, using theoretical arguments, simulated data and real data. 1. Introduction The Self-Organizing Map (SOM) of Teuvo Kohonen ([9], [10]) are used nowadays through numerous domains where it found effective applications by itself or coupled with other data analysis devices (classical factorial data analysis, source separation algorithm, filtering for signal processing, multilayer perceptrons for speech recognition, etc.). See for example [8], [5], [12], [3] etc. for definitions and numerous applications. But it is well known that SOM appears to be a very useful extension (see [1]) of the classical Simple Competitive Learning algorithm (SCL) by adding neighborhood relations between the code-vectors. It is very interesting to keep in mind this property when studying the SOM algorithm. Both SOM algorithm and SCL algorithm are on-line stochastic algorithms, which means they update the values of the code-vectors (or weight vectors) at each step, that is the arrival or presentation of a new observation. These modifications are