Accession Number : AD0691118

Title :   PROPERTIES OF A CLASS OF OBJECTIVE FUNCTIONS IN CLUSTER ANALYSIS.

Descriptive Note : Technical rept.,

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

Personal Author(s) : Smith,Carlos Francisco

Report Date : JUN 1969

Pagination or Media Count : 80

Abstract : The criterion which is used to obtain the best clustering of objects is min F(A) (F(A) is the objective function). It happens frequently in practice that NG, the number of groups at which the global optimum (or best) allocation occurs, is very close to n-1 groups where n denotes the number of objects to be grouped. This suggests a need to measure the value that the analyst gives to reducing the number of groups at which the global optimum occurs. At the same time it also suggests a need for developing additional criteria that would indicate to the user the existence of meaningful allocations occurring at a number of groups smaller than NG. It is shown here that the objective function (F sub K)(A) may be used as a diagnostic tool toward the identification of ill-defined clusters of the data. Properties of the class of objective functions, (F sub K)(A) are presented and discussed. Various examples are presented to illustrate the usefulness of the technique. (Author)

Descriptors :   (*STATISTICAL FUNCTIONS, GROUPS(MATHEMATICS)), SAMPLING, STATISTICAL DATA, ANALYSIS OF VARIANCE, COMPUTER PROGRAMS, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE