Lors de l'analyse de données fonctionnelles, il est bien connu que les 
problèmes de discrimination et de régression sont parfois mieux résolus si
on utilise les dérivées plutôt que les fonctions observées. Nous nous 
proposons de présenter un résultat qui prouve que, dans certaines conditions,
l'utilisation des dérivées permet également d'approcher asymptotiquement 
l'erreur optimale, pour des méthodes de discrimination ou de régression très
générales.
		

In some applications, curve classifiers achieve better performances if they
work on the derivatives of order m of their inputs. Although the use of 
derivatives is a common practice, no theoretical result proves that this 
approach is relevant. More precisely, this paper proves that the use of the 
derivatives instead of the function itself does not lead to a dramatic loss 
of information and that it has no consequence for the convergence of the 
method to the Bayes function. To that aim, we rely on a smoothing spline 
based approach that gives a strong theoretical background to the common 
practice of using derivatives in the realistic case where the observed 
functions are only known by their values on a discrete sampling grid. The 
consistency of a very general derivative based classifier or regression 
scheme is proved.
		

Finding meaningful communities in social network, or, to use a more classical
vocabulary, clustering a graph, is a very important problem in social network
analysis. For very large graphs, a fast clustering algorithm provides a coarse
graining of the graph and can be considered a preprocessing phase before time
consuming algorithms. For small to medium size graphs, communities can be
analyzed manually (or at least semi-automatically) by specialists in order to
figure out the global organization of the underlying social network.
This talk focuses on the second case, when the goal is to display to an end 
user a visual representation of a social network. The main idea of our work 
is to find communities that can be displayed easily on a plane. Our method 
is based on the self-organizing map paradigm.
We first recall briefly some extension of the self-organizing map to kernel 
and dissimilarity data. Then we give examples of kernels and dissimilarities
that can be constructed to compare the nodes of a graph using its link 
structure. We show what type of results can be obtained in this framework on
real world graphs and outline advantages and drawbacks of the method.