Accession Number : AD0694409

Title :   AN AXIOMATIC BASIS AND COMPUTATIONAL METHODS FOR OPTIMAL CLUSTERING.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING

Personal Author(s) : Padron,Mario

Report Date : MAR 1969

Pagination or Media Count : 185

Abstract : This report is concerned with the problem of classifying objects into clusters in such a way that objects within the same cluster are alike and objects in different clusters are relatively dissimilar. A distance or measure of similarity is required in order to measure the degree of likeness of similarity existing between any pair of objects. A clustering criterion or measure of the goodness of any given allocation is developed from basic postulates which attempt to quantify the notions of within group homogeneity and between group heterogeneity. Basic mathematical and experimental properties of the clustering criterion are demonstrated and illustrated. The problem is then imbedded into a mathematical programming formulation which permits the theoretical development of a computational algorithm which converges to an optimal solution for problems of a limited size. With a significant contribution from the algorithm a heuristic method is developed to facilitate the use of the technique for larger problems with a great increase in speed and a very small reduction in accuracy. Several examples are presented to illustrate the properties of the two computational methods developed. Finally, the work presented is compared with other major contributions in this field and suggestions for further research are given. The appendices include three of the major computer programs developed, together with an outline of the problem of grouping objects to minimize an interaction cost, which could be considered a special case of the clustering problem. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, CLASSIFICATION), OPTIMIZATION, ALGORITHMS, PSYCHOLOGICAL TESTS, COMPUTER PROGRAMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE