Some problems in the theory and application of the methods of numerical taxonomy

摘要

Several of the methods of numerical taxonomy are comparedudand shown to be variants of a tripartite grouping procedureudassociated with a generalised intercluster similarity functionudinvolving ten computational parameters. Clustering by the techniques of hierarchic fusion, monothetic division and iterativeudrelocation is obtained using different arithmetic combinationsudof the function parameters to both compute similarities and effectudchanges in cluster membership. The combinatorial solution forudWard's method is found, and the centroid sorting combinatorialudsolution is extended for size difference, shape difference, dispersion and dot product coefficients.ududIt is suggested that clusters are characterised more by theudchoice of similarity criterion than by the choice of method, andudit is demonstrated that some common criteria such as distance andudthe error sum of squares are inclined to force spherical 'minimum-variance' classes. These are contrasted by 'natural' classes,udwhich correspond to closed density surfaces defined for a multi-variate sample space by the underlying probability density function.ududA method for mode-seeking is developed from this probabilisticudmodel through various theoretical and experimental phases, and itudis shown to perform slightly better than iterative relocation withudthe minimum-variance criteria using several Gaussian test populations.ududA fast algorithm is proposed for the solution of theudJardine-Sibson method for generating overlapping classes, and itudis observed that this technique finds natural classes and isudclosely related to the probabilistic model.ududSome aspects of computational procedures are discussed, andudin particular, it is proposed that a generalised system involvinguda statistical language, conversational mode package and program suite could be developed from a basic subroutine system. Paging and simulation techniques for the organisation of direct-accessuddata files are suggested, and a comprehensive package of computerudprograms for cluster analysis is described.