Factor Analysis of Evolution and Cluster Methods on Trajectories

In this paper, we study the evolution of objects indexed by i(i∈I) and associated with the lines of a two-way contingency table, observed at several times. At each time t (t∈T), the j-th column of the slice {n_ijt, i∈J} is associated with the j-th category of one or seveveral qualitative variables. The adaptation of the Factor Analysis of Evolutions (FAE) to such a cube of data, proposed in (5) and (6) produces factors, correlation circles and graphical displays of trajectories in factorial planes. Here, after a brief overview of FAE, we propose a hierarchical agglomerative clustering (HAC) method, which is complementary to FAE. Thus the results of the HAC can be represented by mean of classes of trajectories in the factorial planes found independently using FAE. This allows us to see the agreement between the results of the two methods, and enhances the interpretation of both. In this way, the difficulty of interpreting a large number of trajectories in the factorial planes is overcome by using the HAC method. We apply this classification procedure to the example already analysed in (5) and (6).