The self-organizing map (SOM) [Kohonen, 1982, Kohonen, 1990, Kohonen, 1995c, Kohonen et al., 1996b] is a neural network algorithm that has been used for a wide variety of applications, mostly for engineering problems but also for data analysis (e.g., Back et al., 1996; Blayo and Demartines, 1992; Carlson, 1991; Cheng et al., 1994; Garavaglia, 1993; Martín-del-Brío and Serrano-Cinca, 1993; Marttinen, 1993; Serrano-Cinca, 1996; Ultsch, 1993b; Ultsch and Siemon, 1990; Varfis and Versino, 1992; Zhang and Li, 1993). A comprehensive treatment of the topic is provided by Kohonen (1995c); here only aspects relevant for data exploration and aspects needed for understanding the relationships between the SOM and the other algorithms will be presented.

In this section the data mining tools have been divided into two categories, clustering methods and projection methods. The SOM is a special case in that it can be used at the same time both to reduce the amount of data by clustering, and for projecting the data nonlinearly onto a lower-dimensional display.

The basic algorithm is first motivated with a discussion of competitive learning in Section 6.4.1. Some of its properties that are useful for data analysis are then introduced in Section 6.4.2. Mathematical treatments of the algorithm, and its relations to other algorithms are discussed in Section 6.4.3. Especially two algorithms, the K-means clustering and the principal curves, are very closely related to the SOM. A mathematically oriented reader may wish to concentrate on Section 6.4.3; the algorithm is fully usable without any reference to competitive learning.

- The self-organizing map algorithm
- Properties useful in exploring data
- Mathematical characterizations
- Some variants
- Notes on statistical accuracy

Mon Mar 31 23:43:35 EET DST 1997