Clayton copula and mixture decomposition

A symbolic variable is often described by a histogram. More generally, it can be provided in the form of a continuous distribution. In this case, the problem is to solve the most frequent problem in data mining, namely: to classify the objects starting from the description of the variables in the form of continuous distributions. A solution is to sample each distribution in a number N of points, and to evaluate the joint distribution of these values using the copulas, and also to adapt the dynamical clustering (nuées dynamiques) method to these joint densities. In this paper we compare the Clayton copula and the Normal copula for more than 2 dimensions, and we compare results of clustering by using on the one hand the method based on the Clayton copula and traditional methods (MCLUST, and K-means). Our comparison is based on 2 well-known classical data files.