PROPERTIES OF A CLASS OF OBJECTIVE FUNCTIONS IN CLUSTER ANALYSIS.
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
Pagination or Media Count:
The criterion which is used to obtain the best clustering of objects is min FA FA 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 KA 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 KA are presented and discussed. Various examples are presented to illustrate the usefulness of the technique. Author
- Statistics and Probability