The Construction of Hierarchic and Non-Hierarchic Classifications

Many of the cluster methods that are used in the construction of classificatory systems operate on data in the form of a dissimilarity coefficient on a set of objects. In this paper we outline a theoretical framework within which the properties of such methods may be discussed. Certain conditions that a cluster method should satisfy are suggested, and a particular sequence of cluster methods which satisfies these conditions is described. The application of the sequence of methods is illustrated by a simple example.

[1]  Louis L. McQuitty.  AGREEMENT ANALYSIS: CLASSIFYING PERSONS BY PREDOMINANT PATTERNS OF RESPONSES1 , 1956 .

[2]  D. Rogers,et al.  A Graph Theory Model for Systematic Biology, with an Example for the Oncidiinae (Orchidaceae) , 1966 .

[3]  Raymond E. Bonner,et al.  On Some Clustering Techniques , 1964, IBM J. Res. Dev..

[4]  S. C. Johnson.  Hierarchical clustering schemes , 1967, Psychometrika.

[5]  W. T. Williams,et al.  Dissimilarity Analysis: a new Technique of Hierarchical Sub-division , 1964, Nature.

[6]  G. Estabrook.  A mathematical model in graph theory for biological classification. , 1966, Journal of theoretical biology.

[7]  G. N. Lance,et al.  A General Theory of Classificatory Sorting Strategies: 1. Hierarchical Systems , 1967, Comput. J..

[8]  C. J. Jardine,et al.  The structure and construction of taxonomic hierarchies , 1967 .

[9]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[10]  Robert L. Miller,et al.  A MATHEMATICAL MODEL APPLIED TO A STUDY OF THE EVOLUTION OF SPECIES , 1951 .

[11]  Robert R. Sokal,et al.  The effects of different numerical techniques on the phenetic classification of bees of the Hoplitis complex (Megachilidae) , 1967 .

[12]  R. Sibson,et al.  A model for taxonomy , 1968 .

[13]  R. M. Needham.  Automatic Classification in Linguistics , 1967 .

[14]  Eli C. Minkoff,et al.  The Effects on Classification of Slight Alterations in Numerical Technique , 1965 .

[15]  R. Sokal,et al.  Principles of numerical taxonomy , 1965 .

[16]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[17]  J. Kruskal.  Nonmetric multidimensional scaling: A numerical method , 1964 .

[18]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[19]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[20]  W. T. Williams,et al.  Fundamental Problems in Numerical Taxonomy , 1966 .

[21]  R. Jancey.  Multidimensional group analysis , 1966 .

[22]  W. T. Williams,et al.  A Generalized Sorting Strategy for Computer Classifications , 1966, Nature.

[23]  G. N. Lance,et al.  A general theory of classificatory sorting strategies: II. Clustering systems , 1967, Comput. J..

[24]  J. H. Ward.  Hierarchical Grouping to Optimize an Objective Function , 1963 .

[25]  G. N. Lance,et al.  Computer programs for monothetic classification ("Association analysis") , 1965, Comput. J..

[26]  Robert R. Sokal,et al.  A statistical method for evaluating systematic relationships , 1958 .

[27]  W. T. Williams,et al.  Angiosperm taxonomy: a comparative study of some novel numerical techniques , 1966 .