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On the generalised affinity coefficient for complex data

Bacelar-Nicolau H.

Biocybernetics and Biomedical Engineering

2002

Vol. 22, no. 1

31-42

This paper concerns the affinity coefficient and extensions for maesuring the similarity between data units in classification, when we are dealing with large and complex databases. More precisely we refer to the extended weighted affinity coefficient and its role in hierarchical classification, when we are dealing with a generalised data table where the cells can contain a set of values, describing a probability distribution, a histogram (frequency distribution), or integer frequencies, for instance, instead one single value. Here we study the case of frequency distributions, since in our approach the other cases appear to be derived as a generalisation (integer frequencies, real data, for instance) or else as a particular case (binary data, ordinal data) of this one. Either the weighted affinity coefficient or the probabilistic associated coefficients can be extended, in the clustering viewpoint, to hierarchical (and non-hierarchical) aggregation criteria and aggregation adaptive (parametric) families. An application to a real case is presented.