Article,
An Order Theoretic Model for Cluster Analysis
SIAM Journal on Applied Mathematics, 34 (1): 55--72 (1978)
Abstract
To effectively deal with ordinal clustering problems, an order theoretic model for the subject is presented. It is compared to an earlier graph theoretic model due to N. Jardine and R. Sibson. Some of its salient properties are established, with special attention paid to the incorporation of Jardine and Sibson's "flat" cluster methods into the model. It is shown how the characterization of flat cluster methods leads to a universal mapping problem in the theory of partially ordered sets. This problem is solved, and its solution applied both to the present model and to the Jardine-Sibson model.
