Combinatorial Data Analysis: Optimization by Dynamic Programming
Combinatorial data analysis (CDA) refers to a wide class of methods for the study of relevant data sets in which the arrangement of a collection of objects is absolutely central. The focus of this monograph is on the identification of arrangements, which are then further restricted to where the combinatorial search is carried out by a recursive optimization process based on the general principles of dynamic programming (DP). The authors provide a comprehensive and self-contained review delineating a very general DP paradigm or schema that can serve two functions. First, the paradigm can be applied in various special forms to encompass all previously proposed applications suggested in the classification literature. Second, the paradigm can lead directly to many more novel uses. An appendix is included as a user's manual for a collection of programs available as freeware.
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above-diagonal anti-Robinson form Arabie average proximity between-subset Chapter classes column objects column order combinatorial continuum coordinate representation defined denoted diameter digits discussed dissimilarity DPCL1U DPHI1U DPSE2U Dynamic Programming entities entries F(Ak full partition hierarchy GDPP given gradient conditions greedy heuristic heuristic hierarchical clustering Hubert identified INDEX FOR SUBSET INPUT MATRIX integer joint sequencing least-squares linear loss function LOWER TRIANGULAR MATRIX main diagonal matrix patterning maximize maximum measure of matrix MEMBERSHIP number of object NUMBER OF SUBSETS object order object pairs object sequencing obtained optimal ordered partitions optimal partition hierarchy optimal paths optimal value optimization task options order constraint partial partition hierarchies possible proximity data pSSij recursive process reordered matrix row and column row objects SEriation skew-symmetric matrix skew-symmetric proximity specific SQUARE MATRIX subscripts subset heterogeneity measure symmetric matrix symmetric proximity matrix two-mode proximity ultrametric unweighted gradient weighted gradient measure Ω1 Ω