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 additive constant additive tree ALLPERMS anti-Robinson form block size centroid metric city-block metric COLPERM column object ordering column order convex sets coord coordinates coordtwo CSAR data matrix defines the block defining the row dendrogram diameter diff digits dissimilarity interpretation entries finds and fits fitted values function find given starting permutation heuristic inflection points inperm input beginning permutation input proximity matrix integers iterative projection iterative QA iterative quadratic assignment KBLOCK defines L2-norm least-squares optimal matrix loss function M-function MATLAB matrix using iterative Meulman monotonic transformation monproxpermut multidimensional scaling nrow O O O O object ordering given object pair outperm outpermone outpermtwo partition hierarchy permutation defining permutations identified PROX proximity data PROXTM randperm rawindex reordered row and column ROWPERM SAR matrix ſlS strategy subsets symmetric proximity matrix TARG targone two-mode proximity matrix ultrametric matrix unidimensional scaling usage syntax vafl variance-accounted-for of VAF zero main diagonal