Mathematical Sciences: General Global Criteria for SelectingClustering Algorithms

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This project will develop global criteria for selecting clustering procedures using the admissible clustering approach of Fisher and Van Ness with extended definitions of admissibility conditions. These admissibility conditions will be applied to the general infinite parameterized family of clustering procedures proposed by Lance and Williams; and for each condition, the corresponding subset of the family's parameter space yielding admissible algorithms will be determined. Clustering is a heavily used tool for partitioning a group of objects into subgroups or species. It is used by taxonomists, librarians, epidemiologists, bankers, scientists and many others to classify large, complex sets of objects into homogeneous groups which can be comprehended and handled better. Numerous clustering methods have been proposed over the years, with each giving a different clustering; hence, the choice of algorithm is important. The work here is to codify the various algorithms according to the properties needed for a specific application.