Issue No.02 - February (1972 vol.21)
Warren L. G. Koontz , School of Electrical Engineering, Purdue University, Lafayette, Ind.; Bell Telephone Laboratories, Inc., Holmdel, N. J. 07733.
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 criterion for clustering is derived as a measure of representation error. Some special cases are derived by simplifying the general criterion. A general algorithm for finding the optimum classification with respect to a given criterion is derived. For a particular case, the algorithm reduces to a repeated application 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 finite sample case.
Warren L. G. Koontz, "A Nonparametric Valley-Seeking Technique for Cluster Analysis", IEEE Transactions on Computers, vol.21, no. 2, pp. 171-178, February 1972, doi:10.1109/TC.1972.5008922