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Analysis of the interactions among \(k\) partitions taken 2 by 2: Theory and application in biology. (Analyse des interactions entre \(k\) partitions prises \(2\) à \(2\): théorie et application en biologie.) (French) Zbl 0972.62520
Summary: his paper introduces a new notion of ‘interactions’ between \(n\) partitions \(\mathcal P_1,\mathcal P_2,\cdots, \mathcal P_n\) (with weights \(a_1,a_2,\cdots, a_n\)) on a set \(I\), with respect to a contingency table \(k_{IJ}\), where \(J\) is a set of categorical variables. We propose a method, based on correspondence analysis, to study these interactions. This method covers a large area, including factor analysis of structured tables (between classes analysis and within classes analysis) and multiple correspondence analysis. Some new hierarchical clustering algorithms (under constraints) are also given. Finally, these new methods are applied to a set of biological data.
MSC:
62H17 Contingency tables
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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