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This volume is a logical extension of #11, Multidimensional Scaling, providing an up-to-date overview of some three-way modesl for multidimensional scaling and related techniques.104

The Structural Representation of Proximity Matrices with MATLAB presents and demonstrates the use of functions (by way of M-files) within a MATLAB computational environment to effect a variety of structural representations for the proximity information that is assumed to be available on a set of objects. The representations included in the book have been developed primarily in the behavioral sciences and applied statistical literature (e.g., in psychometrics and classification), although interest in these topics now extends more widely to such fields as bioinformatics and chemometrics.Throughout the book, two kinds of proximity information are analyzed: one-mode and two-mode. One-mode proximity data are defined between the objects from a single set and are usually given in the form of a square symmetric matrix; two-mode proximity data are defined between the objects from two distinct sets and are given in the form of a rectangular matrix. In addition, there is typically the flexibility to allow the additive fitting of multiple structures to either the given one- or two-mode proximity information.This book is divided into three main sections, each based on the general class of representations being discussed. Part I develops linear and circular unidimensional and multidimensional scaling using the city-block metric as the major representational device. Part II discusses characterizations based on various graph-theoretic tree structures, specifically those referred to as ultrametrics and additive trees. Part III uses representations defined solely by order properties, particularly emphasizing what are called (strongly) anti-Robinson forms.

Modern data analysis stands at the interface of statistics, computer science, and discrete mathematics. This volume describes new methods in this area, with special emphasis on classification and cluster analysis. Those methods are applied to problems in information retrieval, phylogeny, medical diagnosis, microarrays, and other active research areas.