Ultrametric Hierarchical Clustering Algorithms | Psychometrika | Cambridge Core (original) (raw)

Abstract

Johnson has shown that the single linkage and the complete linkage hierarchical clustering algorithms induce a metric on the data known as the ultrametric. Through the use of the Lance and Williams recurrence formula, Johnson's proof is extended to four other common clustering algorithms. It is also noted that two additional methods produce hierarchical structures which can violate the ultrametric inequality.

References

Anderberg, M. R. Cluster analysis for applications, 1973, New York: Academic Press.Google Scholar

Cormack, R. M. A review of classification. Journal of the Royal Statistical Society, 1971, 134, 321–367.CrossRefGoogle Scholar

Jardine, N., & Sibson, R. Mathematical taxonomy, 1971, New York: Wiley.Google Scholar

Lance, G. N., & Williams, W. T. A generalized sorting strategy for computer classification. Nature, 1966, 212, 218–218.CrossRefGoogle Scholar

Lance, G. N., & Williams, W. T. A general theory of classificatory sorting strategies: I. Hierarchical systems. Computer Journal, 1967, 9, 373–380.CrossRefGoogle Scholar

Williams, W. T., Lance, G. N., Dale, M. B., & Clifford, H. T. Controversy concerning the criteria for taxonometric strategies. Computer Journal, 1971, 14, 162–165.CrossRefGoogle Scholar