Statistical Physics and the Clustering Problem

This chapter reviews statistical approaches to the clustering problem, i.e. the task of partitioning data-sets in classes in such a way that points in the same class are more similar to one another than to those in other classes. Although this is techni­cally an ill-posed problem, it is of great importance in a wide range of applications and numerous methods have been proposed to tackle it. This paper reviews mainly the coupled maps approach to clustering which performs a non-parametric clas­sification without any assumptions on the distribution of clusters or the number of classes. The technique is illustrated on a biological example (reconstruction of phylogenetic trees) and one from coding theory. The merits of various approaches and the remaining challenges are also discussed.