Asymptotic Analysis of a Nonparametric Clustering Technique
- 1 September 1972
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-21 (9) , 967-974
- https://doi.org/10.1109/tc.1972.5009073
Abstract
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.Keywords
This publication has 6 references indexed in Scilit:
- A Nonparametric Valley-Seeking Technique for Cluster AnalysisIEEE Transactions on Computers, 1972
- Graph-Theoretical Methods for Detecting and Describing Gestalt ClustersIEEE Transactions on Computers, 1971
- Nonparametric feature selectionIEEE Transactions on Information Theory, 1969
- On Some Invariant Criteria for Grouping DataJournal of the American Statistical Association, 1967
- Estimation of a multivariate densityAnnals of the Institute of Statistical Mathematics, 1966
- On Estimation of a Probability Density Function and ModeThe Annals of Mathematical Statistics, 1962