256. Note: An Algorithm for Hierarchical Classifications

An algorithm is given which can be programmed to compute a general classification process for six accepted methods and results derived for the method of optimizing an error sum of squares objective function are derived.

Abstract

SUMMARY The recent interest in numerical classification and its application in the biological sciences to the evaluation of taxa has prompted the introduction of a large number of clustering processes, many of which are justified by empirical results. There is clearly a need for the formulation of a theoretical approach to the subject, and this is aided by the comparison and generalisation of existing processes by analytic methods. The work of Lance and Williams in this direction is supplemented here by results derived for the method of optimizing an error sum of squares objective function, and an algorithm is given which can be programmed to compute a general classification process for six accepted methods.