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T. Kohonen: Self-Organizing Maps

Preface to the Third Edition

After the second edition of this book came out in early 1997, the number of scientific papers published on the Self-Organizing Map has increased from about 1500 to some 4000. Also two special workshops dedicated to the SOM have been organized, not to mention numerous SOM sessions in neural-network conferences. In view of this growing interest it was felt desirable to make extensive revisions to this book. They are of the following nature.

Statistical pattern analysis has now been approached more carefully than earlier. A more detailed discussion of eigenvectors and eigenvalues of the symmetric matrices, which are the ones usually encountered in statistics, has been carried out in Sect. 1.1.3; also new probabilistic concepts, to mention factor analysis, have been discussed in Sect. 1.3.1. A survey of projection methods (Sect. 1.3.2) has been added, in order to relate the SOM to classical paradigms.

Vector Quantization has now been discussed in one main section, and derivation of the point density of the codebook vectors using the calculus of variations has been added, in order to familiarize the reader with this otherwise complicated statistical analysis.

It was also felt that the discussion of the neural-modeling philosophy should include a broader perspective of the main issues. A historical review in Sect. 2.2, and the general philosophy in Sects. 2.3., 2.5., and 2.14 are now expected to help especially the newcomers to orient themselves better amongst the profusion of contemporary neural models.

The basic SOM theory in Chap. 3 has now first been approached by a general qualitative introduction in Sect. 3.1. Other completely new concepts discussed in Chap. 3 are the point density of the model vectors (Sect. 3.12) and the interpretation of the SOM mapping (Sect. 3.16).

Only modest revisions have been made to Chap. 4.

Among the new variants in Chap. 5, the SOM of symbol strings (and other nonvectorial items) has been discussed in Sect. 5.7, and a generalization of the SOM in the direction of evolutionary learning has been made in Sect. 5.9.

To Chap. 6, the batch-computation scheme of the LVQ1 has been added.

In Chap. 7, a major revision deals with a new version of WEBSOM, the SOM of large document files, by which it has been possible to implement one of the most extensive ANN applications ever made, namely, the SOM of seven million patent abstracts. The amount of text thereby mapped is 20 times that of the Encyclopaedia Britannica!

The most visible and often desired addition to the third edition is the new Chapter 8 on software tools that is hoped to be useful for practitioners.

It was not possible, however, to extend the survey of new SOM applications much beyond that already published in the second edition. A new hardware implementation has been discussed at the end of Chap. 9, but the main change made to the literature survey in Chap. 10 is its reorganization: the taxonomy and indexing of its contents is now more logical than in the second edition.

In the Preface to the first edition I gave an advise for the first reading of this book. Since the numbering of the sections has now changed, the new recommended reading sequence for a short introductory course on the SOM is the following: 2.2, 2.9, 2.10, 2.12, 3.1-3, 3.4.1, 3.5.1, 3.6, 3.7, 3.13, 3.14, 3.15, 6.1, 6.2 (skipping the derivation), 6.4-9, 7.1 and 7.2.

Again I got much help in the revision from my secretary, Mrs. Leila Koivisto; I am very much obliged to her. Some parts of the word processing were made by Mr. Mikko Katajamaa. Naturally I have benefited from the good scientific work done by all my younger colleagues in our university. Dr. Samuel Kaski has kindly allowed me to use in Sect. 1.3.2 material compiled by him.

After writing all the three editions, I want to once again express my gratitude to the Academy of Finland for allowing me to carry out this writing under their auspices.

Espoo, Finland       Teuvo Kohonen
May, 2000

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Monday, 29-Jan-2001 15:25:50 EET