Symbolic object description of strata by segmentation trees (Q1584170)

Tree-growing methods or segmentation trees are in general recursive nonparametric classification methods that, at each step, obtain the binary partition in the population, which maximises an information content measure of the new splits with respect to predefined classes. Several information criteria are proposed in the literature. Frequently, the underlying population is not only subdivided into the classes to be investigated, but is simultaneously composed of groups of individuals, which are called strata, such as when individuals of a country are divided into regions, individuals of a region are divided into towns, companies are divided into economic sectors, etc. Then, it is interesting to explain how strata influence the classification rules obtained by a tree-segmentation method. Some rules are applicable to some strata, and others are not. The aim of this paper is: (i) to predict or to explain the value of the criterion variable for individuals by the predictors, conditioned on the stratum; (ii) to explain how these predictions are affected by stratum membership; (iii) to detect sets of strata for which this explanation is the same; (iv) to describe a stratum symbolically by the set of rules which apply to it with their importance. As output of the authors' algorithm, each input stratum or class of individuals is described by a set of symbolic objects which describe different ``segments'' of objects characterized by the values of their variables as well as by certain percentages. The algorithm is applied to classical data and to parabolistic data input descriptions of individuals.