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The Structural Representation of Proximity Matrices with MATLAB (Paperback, Illustrated Ed)
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The Structural Representation of Proximity Matrices with MATLAB (Paperback, Illustrated Ed)
Series: ASA-SIAM Series on Statistics & Applied Probability, No. 19
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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.
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