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Learning hierarchical clustering from examples. Application to the adaptive construction of dissimilarity indices. (English) Zbl 0564.62052
The paper is devoted to studies on hierarchical clustering methods where dissimilarity indices are constructed on the basis of the recurrence formula, \[ \delta (h,h_ 1\cup h_ 2)=a_ 1\delta (h,h_ 1)+a_ 2\delta (h,h_ 2)+a_ 3\delta (h_ 1,h_ 2)+ \] \[ a_ 4f(h)+a_ 5f(h_ 1)+a_ 6f(h_ 2)+a_ 7| \delta (h,h_ 2)-\delta (h,h_ 1)| \] where \(\delta\) stands for the dissimilarity index and h, \(h_ 1\), \(h_ 2\) are hierarchies indexed by f. The choice of the dissimilarity index (determined by coefficients \(a_ i\), \(i=1,2,...,7\), is performed with respect to some learning set of data. Moreover, necessary and sufficient conditions for non-existence of inversions are studied.
Reviewer: W.Pedrycz
MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
68T10 Pattern recognition, speech recognition
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