Many fields of research are confronted one day with this same problem: to highlight a structure, a simplified and ordinate representation of the world, where there is disorder and incomprehension.

For example, the biologist want to group various molecules according to their effects on various genes; the economist want to be able to distinguish the healthy companies from the companies in bankruptcy; the geographer is interested in identifying with certainty the fields, the forests on a satellite image. All these problems have a common point which bears a name: classification.

The problems of classification are divided into two parts: supervised classification (still called dsicriminant analyzis) and unsupervised classification (still called simply classification or clustering). The discriminating analysis consists in assigning a new observation to existing groups: it thus seeks to explain a qualitative variable starting from information contained in explanatory variables. Classification tries to recognize groups (or classes) among a set of observations, so that two entities in the same cluster are closer than two objects in two different groups.

The unit of Statistics is interested as well in the problems of discriminating analysis as in the problems of clustering. While resting on the only assumption that the observations are distributed according to a Poisson process, various algorithms are developed and studied: theoretical properties, computational and memory costs, convergence). Finally, thanks to the various collaborations of the Unit of Statistics, these new methods are applied to various problems: early prediction of bankruptcies of companies, teledetection, recognition of form.

The tools used in the development of these methods are very varied: nonparametric estimations of density by the histograms, by kernels, by wavelets, discrimination trees. Other research in progress try to extend the applicability of these algorithms to the classification of symbolic data and classification of time series. Methods allowing the determination of the number of classes are also studied.

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