Abstract
This work comes within the field of data analysis using Galois lattices. We consider ordinal, numerical single or interval data as well as data that consist on frequency/probability distributions on a finite set of categories. Data are represented and dealt with on a common framework, by defining a generalization operator that determines intents by intervals. In the case of distribution data, the obtained concepts are more homogeneous and more easily interpretable than those obtained by using the maximum and minimum operators previously proposed. The number of obtained concepts being often rather large, and to limit the influence of atypical elements, we propose to identify stable concepts using interval distances in a cross validation-like approach.

Abstract
In this paper we propose a divisive top-down clustering method designed for interval and histogram-valued data. The method provides a hierarchy on a set of objects together with a monothetic characterization of each formed cluster. At each step, a cluster is split so as to minimize intra-cluster dispersion, which is measured using a distance suitable for the considered variable types. The criterion is minimized across the bipartitions induced by a set of binary questions. Since interval-valued variables may be considered a special case of histogram-valued variables, the method applies to data described by either kind of variables, or by variables of both types. An example illustrates the proposed approach.

Abstract

Abstract
We study assertion objects that constitute a particular class of symbolic objects. Symbolic objects constitute a data analysis driven formalism, which can be compared to propositional calculus, but which is oriented toward the duality intension (characteristic properties) versus extension (set of all individuals verifying a given set of properties). The set of assertion objects is endowed with a partial order and a quasi-order. We focus on the property of completeness, which precisely expresses the duality intension-extension. The order structure of complete assertion objects is studied, using notions of lattice theory and Galois connection, and extending Wille's work to multiple-valued data. Two results are then obtained for particular cases.

Abstract
This paper introduces symbolic data analysis, explaining how it extends the classical data models to take into account more complete and complex information. Several examples motivate the approach, before the modeling of variables assuming new types of realizations are formally presented. Some methods for the (multivariate) analysis of symbolic data are presented and discussed. This is however far from being exhaustive, given the present dynamic development of this new field of research. Copyright © 2011 Wiley Periodicals, Inc., A Wiley Company.

Abstract
Applying graph theory to clustering, we propose a partitional clustering method and a clustering tendency index. No initial assumptions about the data set are requested by the method. The number of clusters and the partition that best fits the data set, are selected according to the optimal clustering tendency index value.