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Reviewer: V. Vemuri

This third edition is the latest incarnation of a book that first appeared in 1977. Kohonen takes pains to point out that the associative memories discussed here are different from the traditional content-addressable memories, “the memory locations of which are selected by parallel search.” In the authors words, this book “provides a tutorial treatment of new approaches to self-organization, adaptation, learning and memory and lends itself to graduate and post-graduate courses in information science, computer science, psychology, theoretical biology and physics.” The books 312 pages include 100 figures, 339 references, and a subject index, but no exercises. The author gives only one 20-line computer program, written in BASIC. In view of the nature of the mathematical content, this book is more likely to appeal to electrical engineers and physicists than to computer scientists. The book is organized into ten chapters and can be divided into three parts. The first part, comprising the first three chapters, is essentially a review. The next four chapters constitute the essence of the book, while the last three chapters discuss issues that, although important, appear peripheral to the central theme of the book. Chapter 1, “Various Aspects of Memory” (29 pages), treats the concept of memory from biological, electronic, mathematical, and logical viewpoints. Chapter 2, “Pattern Mathematics” (37 pages), is a brisk review of concepts from linear algebra and a discussion of various distance measures. This chapter assumes that the reader already has some knowledge of linear algebra and a passing familiarity with differential equations. Chapter 3, “Classical Learning Systems” (14 pages), is an even brisker review of Rosenblatts perceptron [1], Widrows Adaline [2], and Steinbuchs learning matrices [3]. Chapter 4, “A New Approach to Adaptive Filters” (36 pages), is a mathematical description of the neural network viewpoint of adaptation. The central idea here is to first write an equation for the output &eegr; i of neuron i as h i = j=1 h m ij x j in terms of the synaptic weights &mgr; j and the inputs &xgr; j and then adjust the weights according to 6 m i 6 t = f x- g m where x =(&xgr; 1 ,…,&xgr; n ) T and M i =(&mgr; i 1 ,…&mgr; in ) T . Using different functional forms for f and g , Kohonen derives a case resulting in the so-called novelty filter and two other cases resulting in a Riccati equation and a Bernoulli equation. He then proceeds with an in-depth development of the novelty filter. In chapter 5, “Self Organizing Feature Maps” (38 pages), the author argues that the introduction of lateral feedback (inhibition as well as excitation) causes the activity of the network to cluster around the local maximum of the input. The rest of the chapter concentrates on topology-preserving mappings. Chapter 6, “Optimal Associative Mappings” (27 pages), focuses on linear and nonlinear associations and the relation between associative mappings on the one hand and regression and estimation techniques on the other. The chapter concludes with a brief discussion of correlation matrix memory. Chapter 7, “Pattern Recognition” (25 pages), presents only those aspects of pattern recognition that the author believes to be relevant to self-organization and associative memory. Familiarity with probabilistic and statistical notions is essential to come to grips with the material discussed in chapters 6 and 7. The third part of the book begins with chapter 8, “More About Biological Memory” (31 pages). Chapter 9, “Notes on Neural Computing” (28 pages), is a meditation on the niche of neural computational paradigms within modern computer science. Finally, chapter 10, “Optical Associative Memories” (16 pages), discusses the highlights of the advances made in holography and optical computing, with special emphasis on optical technologys role in associative memories. How well does the author meet his goal Although the neural network market is inundated with books and review papers, I have had difficulty finding a book suitable for classroom instruction. Kohonens book comes close to filling that need, but not to my complete satisfaction. Inclusion of a few illustrative examples and a set of exercises would have filled one obvious void. The 339 items cited in the references include only one reference to the Hopfield net and one to Grossbergs work. Although I agree with the point of view taken by the author, a passing reference to the above two schools of thought, which have received widespread attention in recent times, would have improved the books pedagogical value. Nevertheless, I am planning to use it on a trial basis in my neural networks class.