Shape from statistics

As Vapnik, the Russian mathematician, once said: "There is nothing so practical as a good theory". This quote seems well-suited to the science of statistical pattern recognition. Brian Ripley, a well-known figure in statistical circles, has, in his new book Pattern Recognition and Neural Networks, given a grand overview of both the theory and the practice of the field and has not skimped in an effort to describe its applicability to a wide range of data analysis problems.

Until the past five years, perhaps, the two-part title of the book would have indicated a two-part book, the first part covering pattern recognition and the second neural networks. Recently, however, and in part due to the actions of Ripley and others whose interests lean toward statistics, a large number of neural network taxonomies may be seen, if wanted, as lying within the field of statistical estimation theory. It is within this framework that Ripley is best poised to detail his experience and understanding.

The task he attempts is not to be underestimated. Both statistical pattern recognition and neural networks are wide fields with many, often contradictory facets and a single volume combining both may seem at first sight over-ambitious. By and large, however, Ripley succeeds admirably.

The book opens with introductory material regarding pattern recognition and its applications and goes on to describe several "real-world" data sets - used throughout the book to detail and compare techniques - which are easily accessible over the Internet. Up to this point one may be forgiven for assuming that Ripley's book was going to contain little mathematics, but this notion has to be quickly abandoned.

Ripley's subsequent analysis is principled and rigorous, but much theoretical development has, I suspect, had to be dropped for the sake of space. For many the level of mathematical knowledge that is assumed may be off-putting, but the field Ripley is detailing is, by necessity, mathematical in nature.

He makes, from time to time, attempts to provide a more immediate accessibility to some concepts. These are, for the main part, successful although a background knowledge of basic statistics is still presupposed, as would be expected. Needless to say, with the compactness of many of the derivations in the book it is necessary from time to time to follow up several of the original references to achieve a full understanding of the arguments.

From chapter two onwards the book continues to consider statistical decision theory, from linear discriminant analysis through to the issues of regularisation and parametric function fitting.

At this point the reader may begin to wonder where the neural networks are. The way for them has, in fact, been cleverly paved so that by the time they are met a thorough understanding of the principles behind their design and functioning exists.

If one wants, however, information regarding the biological metaphors and interpretations surrounding certain aspects of neural network research, then this is not the book to read. Ripley makes but a glancing comment about the original (biological) motivations and interpretations behind neural networks, preferring to keep well within the statistical framework that he has constructed. Indeed, although one can argue that some further neural network methods are encountered later in the book (learning vector quantisation and self-organising maps, for example), they are somewhat in disguise and chapter five ends with a brief, but informative, review of feed-forward networks.

Indeed, to be true to the latter half of the title of the book, several further neural network topics ought, perhaps, to have been included. Ripley does not, for example, consider the important field of recurrent networks and their relation to hidden Markov models nor methods based on fully interconnected networks, such as the Hopfield net.

While this streamlining is well in tune with the thesis of the book, it is perhaps symptomatic of the Balkanisation of the neural network field in general. The rest of the book deals with the important topics of Bayes networks and graphical methods and methods of visualisation, clustering, feature extraction and relevance determination. Although these topics do not wholeheartedly fall within the scope of neural network or pattern recognition methods per se, they are of such vital importance to the successful analysis of data that Ripley's decision to present them is well guided.

Ripley has chosen to include in appendices a more detailed description of areas he refers to as "statistical sidelines". These include such important topics as maximum-likelihood estimation.

A glossary is also provided which acts very efficiently as a dictionary for those less accustomed to the language of statistics (what is the difference between a plug-in and a predictive estimator, for example?) The reference list, as would be expected in a book which covers such wide topics, is extensive and provides an ideal source of primary references for any researcher.

Ripley's book sets out to be a self-contained introduction and reference to pattern recognition and neural networks. While it provides an excellent and well-researched text one must be aware that no mention is made of some, perhaps less fashionable methods of pattern recognition and neural networks. If the book is to provide the backbone of a lecture course on the subject then these topics may need to be covered using another text. The lack of worked examples and set problems may also be a drawback.

The book is, however, of benefit to anyone who has an interest in a principled approach to statistical data analysis. Ripley's intended audience is therefore large and for most of his readers the book will indeed provide an excellent reference for many years to come.

Stephen Roberts is lecturer in electrical and electronic engineering, Imperial College, London.