, and be the pairwise distances between clusters , , and , respectively, be the distance between the new cluster and . An algorithm belongs to the Lance-Williams family if the updated cluster distance can be computed recursively by where and are parameters, which may depend on cluster sizes, that together with the cluster distance function determine the clustering algorithm. Several standard clustering algorithms such as single linkage, complete linkage, and group average method have a recursive formula of the above type. A table of parameters for standard methods is given by several authors.<ref>Cormack, R. M. (1971), "A Review of Classification", Journal of the Royal Statistical Society, Series A, 134(3), 321-367.</ref>Milligan, G. W. (1979), "Ultrametric Hierarchical Clustering Algorithms", Psychometrika, 44(3), 343–346. Ward's minimum variance method can be implemented by the Lance–Williams formula. For disjoint clusters and with sizes and respectively: Hence Ward's method can be implemented as a Lance–Williams algorithm with Variations The popularity of the Ward's method has led to variations of it. For instance, Wardp introduces the use of cluster specific feature weights, following the intuitive idea that features could have different degrees of relevance at different clusters. References Further reading Everitt, B. S., Landau, S. and Leese, M. (2001), Cluster Analysis, 4th Edition, Oxford University Press, Inc., New York; Arnold, London. Hartigan, J. A. (1975), Clustering Algorithms, New York: Wiley. Jain, A. K. and Dubes, R. C. (1988), Algorithms for Clustering Data, New Jersey: Prentice–Hall. Kaufman, L. and Rousseeuw, P. J. (1990), Finding Groups in Data: An Introduction to Cluster Analysis'', New York: Wiley. Cluster analysis algorithms