The Structural Representation of Proximity Matrices with MATLAB presents and demonstrates the use of functions within a MATLAB computational environment, affecting various 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, although interest in these topics now extends more widely to such fields as bioinformatics and chemometrics. 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.
Preface; Part I. (Multi- and Unidimensional) City-Block Scaling: 1. Linear unidimensional scaling; 2. Linear multidimensional scaling; 3. Circular scaling; 4. LUS for two-mode proximity data; Part II. The Representation of Proximity Matrices by Tree Structures: 5. Ultrametrics for symmetric proximity data; 6. Additive trees for symmetric proximity data; 7. Fitting multiple tree structures to a symmetric sroximity matrix; 8. Ultrametrics and additive trees for two-mode (rectangular) proximity data; Part III. The Representation of Proximity Matrices by Structures Dependent on Order (Only): 9. Anti-Robinson matrices for symmetric proximity data; 10. Circular anti-Robinson matrices for symmetric proximity data; 11. Anti-Robinson matrices for two-mode proximity data; Appendix; Bibliography; Indices.
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