Abstract
Critchley and Van Cutsem [7] recently developed the properties of dissimilarities and ultrametrics with values in an ordered set. This theoretical definition allows consideration of a pair of ultrametrics as a two dimensional ultrametric with values in ℝ+ × ℝ+, and provides a good framework to study the dependence between two ultrametrics. In this paper, we just present the basic definitions for introducing the definition of some new indices of dependence or of comparison of two real-valued ultrametrics. Details can be found in Benkaraache’s thesis [4].
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Benkaraache, T., Van Cutsem, B. (1994). Comparison of hierarchical classifications. In: Diday, E., Lechevallier, Y., Schader, M., Bertrand, P., Burtschy, B. (eds) New Approaches in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51175-2_8
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