A Nonparametric Valley-Seeking Technique for Cluster Analysis

The problem of clustering multivariate observations is viewed as the replacement of a set of vectors with a set of labels and representative vectors. A general c r i ter ion for clustering is derived as a measure of representation error. Some special cases are derived by simplifying the general c r i te r ion . A general algorithm for f inding the optimum classi f icat ion with respect to a given cr i ter ion is derived. For a part icular case, the algorithm reduces to a repeated applicat ion of a straightforward decision rule which behaves as a valley-seeking technique. Asymptotic properties of the procedure are developed. Numerical examples are presented for the f i n i t e sample case.