Assigning Objects to Classes of a Euclidean Ascending Hierarchical Clustering

Abstract

In a Euclidean ascending hierarchical clustering (ahc, Ward’s method), the usual method for allocating a supplementary object to a cluster is based on the geometric distance from the object-point to the barycenter of the cluster. The main drawback of this method is that it does not take into consideration that clusters differ as regards weights, shapes and dispersions. Neither does it take into account successive dichotomies of the hierarchy of classes. This is why we propose a new ranking rule adapted to geometric data analysis that takes the shape of clusters into account. From a set of supplementary objects, we propose a strategy for assigning these objects to clusters stemming from an ahc. The idea is to assign supplementary objects at the local level of a node to one of its two successors until a cluster of the partition under study is reached. We define a criterion based on the ratio of Mahalanobis distances from the object–point to barycenters of the two clusters that make up the node.

We first introduce the principle of the method, and we apply it to a barometric survey carried out by the cevipof on various components of trust among French citizens. We compare the evolution of clusters of individuals between 2009 and 2012 then 2013.