The Structural Representation of Proximity Matrices with MATLAB
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.
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addcon addconone addcontwo additive constant additive tree ALLPERMS anti-Robinson form Arabie block size centroid metric circular anti-Robinson cirfitac colperm column object ordering column order confirmatory convex sets coord coordinates coordtwo CSAR data matrix defines the block dendrogram diff digits dissimilarity interpretation entries finds and fits fitted values function find given starting permutation goldfish receptor heuristic Hubert inflection points inperm input proximity matrix iterative projection iterative QA iterative quadratic assignment KBLOCK defines L2-norm least-squares optimal matrix loss function M-file M-function MATLAB matrix using iterative matrix with variance-accounted-for Meulman monotonic transformation monproxpermut multidimensional scaling n x n nrow nS integers O O O O object ordering given object pair outperm outpermone outpermtwo permutation defining permutations identified prox proximity data PROXTM randperm rawindex reordered row and column rowperm strategy subsets symmetric proximity matrix TARG targone targtwo two-mode proximity matrix ultrametric matrix unidimensional scaling vafl variance-accounted-for of VAF zero main diagonal