Asymptotic Analysis of a Nonparametric Clustering Technique

A family of nonparametric clustering criteria has been previously proposed by the authors. One particular member of this family was subjected to analysis and experimentation. This criterion was shown by heuristic argument, experimentation, and approximate asymptotic analysis to exhibit ``valley-seeking´´ behavior. In this paper, we consider a more general class of valley-seeking criteria. The results bear a close resemblance to Parzen´s theory of probability density estimation. This similarity is exploited to develop sufficient conditions for a criterion to be valley seeking in the asymptotic sense.