Advances in Self-Organizing Maps

The Self-Organizing Map (SOM) with its related extensions is the most popular artificial neural algorithm for use in unsupervised learning, clustering, classification and data visualization. Over 5000 publications have been reported in the open literature, and many commercial projects employ the SOM as a tool for solving hard real-world problems. Every two years, the “Workshop on Self-Organizing Maps” (WSOM) covers the new developments in the field. TheWSOM series of conferences was initiated in 1997 by Professor Teuvo Kohonen, and has been successfully organized in 1997 and 1999 by the Helsinki University of Technology, in 2001 by the University of Lincolnshire and Humberside, and in 2003 by the Kyushu Institute of Technology. The Université Paris 1 Panthéon Sorbonne (SAMOS-MATISSE research centre) organized WSOM 2005 in Paris on September 5–8, 2005. The Paris WSOM conference was very successful, with 150 participants, coming from more than 23 countries from all continents (even from Australia). With the help of nice weather and good wine, the atmosphere was studious as well as friendly thanks to the high level of the communications and to the social program (in particular on the first floor of the Eiffel Tower). The Self-Organized Maps community had once again the opportunity to meet and to share knowledge and expertise. Since the first publications, the SOM algorithm as defined by Teuvo Kohonen in the 1970s has seen substantial development. Nowadays, it is used as well as other classical methods for a lot of data mining tasks (classification, clustering, reduction of dimension, descriptive statistics, nonlinear projection, time series analysis, missing data completion, inquiry exploitations, visualization of high dimensional data, etc.). Its mathematical properties have been more deeply studied, even if work remains to be done. A lot of modifications of the original algorithm have been defined in order to allow a more complete theoretical study, or to obtain some interesting properties. The range of its applications has not stopped increasing, having recently touched the economic and management sciences. Many years and several thousands of scientific papers after the first publications on self-organized maps, there is still important activity in the development of new algorithms and methods aimed at building self-organized, topographic maps. In this issue, Kohonen himself proposes a new selforganizing system that can produce superimposed responses to superimposed stimulus patterns. This principle can be used for instance to model pointwise neural projections such