Hierarchical classification of mathematical structures

Abstract

The application area of the methods of cluster analysis has largely developed during the last fifteen years. Nevertheless, the applications of cluster analysis were always made on concrete data resulting from experiments, observations, or more simply, from simulations. This paper presents an application of hierarchical clustering to exact mathematical structures. On the one hand the set of formal series of defined on a field, on the other hand the set of integers fit with the p-adic distance. In addition to a purely technical aspect, the aim of this work is also to show how, and in what way, cluster analysis enables us to understand the structure of a strictly organized data set.