---
title: "A Nonparametric Valley-Seeking Technique for Cluster Analysis"
authors:
  - "Warren L. G. Koontz"
  - "Keinosuke Fukunaga"
doi: ""
url: "https://ijcai.org/proceedings/1971/42"
pdf: "https://ijcai.org/proceedings/1971/0042.pdf"
venue: "Proceedings of the Second International Joint Conference on Artificial Intelligence"
year: 1971
pages: "411-416"
track: ""
keywords:
---

# A Nonparametric Valley-Seeking Technique for Cluster Analysis

Warren L. G. Koontz, Keinosuke Fukunaga

*Proceedings of the Second International Joint Conference on Artificial Intelligence*, pages 411-416.

## Abstract

The probl .. of clustering .ultivsriate observation• il viewed a1 the replacement of a 1et of vector• with a 1et of label• and repre1entative vector•. A general criterion for clu1tering i1 derived as · a mea1ure of repre1entation error. Some 1pecial ease• are derived by 1iaplifying the general criterion. A general algorithm for finding the optimum cla11ification with reapeet to a given criterion 11 de_rived. For a p1rtieular ease, the algorithm reduces to a repeated application of a 1traightforward deei1ion rule which behave• as a valley-leeking technique. A1ymptotic propertiel of the procedure are developed. Numerical examples are pre1ented for the finite uaple case.