A new approach for analyzing a set of hierarchies

The aim of this presentation is to propose a new approach for analyzing hierarchies issued from unsupervised classifications performed on the same (statistical) individuals. This issue has already been partially addressed by several authors for the comparison of different classifications methods (Leclerc (1985), Leclerc and Cucumel (1987) or the special issue of Journal of Classification (Vol. 3, 1986) dedicated to the comparison and consensus of classifications). The starting point of our research framework is the hierarchical sorting task commonly used in psychology and sensory analysis. This method consists in asking subjects to provide each their own hierarchical tree from the same given set of objects. This hierarchical tree is constructed mostly in a binary and descending way: the subjects are asked to divide the objects into two homogeneous groups and then to divide again each of the two groups until they consider the final groups homogeneous. The main feature of this method is that each subject uses his/her own criteria for making these successive divisions. In this kind of experiment were interested into getting a consensus representation of the objects from all the subjects as well as a representation of the subjects, function of the way they classified the objects. In this talk, we propose a method which provides on the one hand a Euclidean representation of the objects and on the other hand a Euclidean representation of the hierarchies (i.e. a subject can be assimilated to his/her hierarchy) linked to the previous one in the manner of Multiple Factor Analysis (MFA, Escofier and Pagès (1998)). This hierarchy representation allows to visualize the different steps taken by each subject and to understand in a certain way his/her cognitive process