Fundamentals of Artificial Neural Networks [Book Reviews]

There is no such thing as too much of a good thing-at least when it comes to well written and comprehensive graduate level texts in any technical field that has been growing as fast as neural computing. In recent years there has been a proliferation of neural network related textbooks that ’attempt to give a broad, mathematically rigorous introduction to the theory and applications of the field for an audience of either professional engineers, graduate students, or both. Among the most notable and recent perhaps are the excellent texts by Haykin [l], Zurada [2], Kung [ 3 ] , and Hertz et. al. [4]. Add to this dozens of volumes of paper collections, and expositions from different perspectives (AI, physics, cognitive science, VLSI (very large scale integration), and parallel processing, etc.), as well as other textbooks, and you rapidly converge to the global minimum: so many books, so little time! If you are interested in learning about the underlying theory of neural computation, however, then perhaps alongside your perusal of the above texts you should also look at yet another one. Fundamentals of ArtiJcial Neural Networks emphasizes fundamental theoretical aspects of the computational capabilities and learning abilities of artificial neural networks (ANN’S). The book is intended for either first year graduate students in electrical or computer science and engineering, or practicing engineers and researchers in the field. It has evolved from a series of lecture notes of two courses on ANN’S taught by the author over the past six years at Wayne State University. Apart from the usual prerequisites of mathematical maturity (probability theory, differential equations, linear algebra, multivariate calculus), the reader is assumed to be familiar with system theory, the concept of a “state,” as well as Boolean algebra and switching theory basics. The author himself is a well-established researcher in the field, with dozens of papers to his credit. The book is well organized and presented, and a delight to read. Exercises at the end of each chapter (some 200) complement the text, and range in difficulty level from the very basic to mathematically or numerically challenging. About 700 relevant references are also provided at the end of the book. The book is centered on the idea of viewing ANN’S as nonlinear adaptive parallel computational models of varying degrees of complexity. Accordingly, the author starts out in Chapter 1 by an exposition of the computational capab es of the simplest models, namely linear and polynomial threshold gates. This is built upon basic concepts of switching theory. The discussion is then extended to the capacity and generalization ability of threshold gates via a proof of the function counting theorem. The treatment is coherent and mathematically rigorous Chapter 2 picks up from the discussion in Chapter 1 by considering networks of linear threshold gates (LTG’s) as well as neuronal units with nonlinear activation functions, and investigates their mapping capabilities. Important theoretical results on bounds on the number of functions realizable by a feedforward network of LTG’s, as