Statistical geometry and classification: Tools for each other
This paper shows some relationships between statistical geometry and classification rules. The first conclusion given is that whatever area one is considering, it is always an expansion of the convex hull of the sample from its centroid. Part two of the paper describes some aspects of classification and discrimination for convex clusters, such as the partitioning problem, the maximum likelihood solution to the clustering problem with corresponding discriminant rules and statistical geometry as a rule. In Part three it is shown how to estimate the inside-outside version of the convex support of a uniform distribution using the classical approach and discriminant analysis.NEWLINENEWLINENEWLINEPart four demonstrates how classification and discriminant analysis for nonconvex clusters work. The partitioning problem is reformulated, and then the maximum likelihood solution to the clustering problem and corresponding discriminant rules are given. Finally an open problem on the estimation of the nonconvex support of a uniform distribution is presented. Graphical examples illustrate the problems handled in the paper. Exact mathematical proofs are not given for most problems.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00040].
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