A Model for Ordinal Nonhierarchical Cluster Methods.
Abstract
Hierarchical clustering involves the creation of a nested sequence of partitions of a set, whereas nonhierarchical clustering deals with a single partition. Nonhierarchical cluster techniques come up in a variety of situations involving such items as: (i) the assignment of stars to galaxies, (ii) the assignment of grades to students by an instructor; (iii) the classification of psychiatric patients by diagnostic type; (iv) the classification of rock formations: (v) the interpretation of LANDSAT images; (vi) automatic target detection; (vii) the grouping of companies according to properties that their stock might have in the stock market. It is not our purpose here to survey the literature in this area - rather, the reader is referred to standard references. As in our earlier model for hierarchical clustering, the viewpoint here will be that the input data has only ordinal significance. The order theoretic properties of the resulting model are offered in Section 2 and it will be related to some earlier theoretical work in Section 3. Finally, Section 4 presents an abstract characterization of the model in terms of semiBoolean algebras.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1981
- Accession Number
- ADA107111
Entities
People
- M. F. Janowitz
Organizations
- University of Massachusetts Amherst