Inversions en classification hiérarchique: Application à la construction adaptative d’indices d’agregation. (English) Zbl 0538.62052

Diday, Edwin

Rev. Stat. Appl. 31, No. 1, 45-62 (1983).

We say that there is an inversion in a hierarchy if the height of a cluster merged later in the hierarchy is lower than that of clusters merged earlier. We give: 1) Necessary and sufficient conditions on the parameters of the G. C. Lance and W. T. Williams formula (1966), generalized by M. Jambu (1978) which insure the existence or non existence of inversion in a hierarchy; one of those new results generalizes the conditions given by P. Ducimetière (1971), G. Milligan (1979) and V. Batagelj (1981).
2) A necessary and sufficient condition on the same parameters which insures the ”neighbourhood reducibility” property of M. Bruynooghe (1978) and thus permits the use of an accelerated algorithm for hierarchical clustering. By using those results and taking account of the a priori knowledge of the user we show that it is possible to obtain adaptive ultrametrics. This work arises towards learning hierarchical clustering from examples [see the author and J. V. Moreau, Learning hierarchical clustering from examples. (1984)].

MSC:

62H30

Classification and discrimination; cluster analysis (statistical aspects)

Keywords:

hierarchical learning; neighbourhood reducibility; accelerated algorithm; hierarchical clustering; adaptive ultrametrics

Citations:

Zbl 0419.62058

References:

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