ABSTRACT
The aim of the symbolic approach in data analysis is to extend problems, methods, and algorithms used on classical data to more complex data called “symbolic”, which are well adapted to represent clusters, categories, or concepts (Diday 2005 [97]). Concepts are defined by intent and an extent that satisfy the intent. For example, the swallow’s species can be considered as a concept, the intent is the description of this species of birds, and the set of swallows is the extent of this concept. Symbolic data are used in order to model concepts by the so called “symbolic objects”. We mention the definition of three kinds of symbolic objects: events, assertions, and synthesis objects. We focus on synthesis objects. For example having defined vases by their color, size, material, etc., and flowers described by their species, type, color, stem, etc., our aim is to find “synthesis objects”, which associate together the most harmonious vases and flowers. This approach can also be applied in the fashion domain in
order to improve clothes of a mannequin, or in advertizing in order to improve the objects represented in a poster. More formally, we consider several objects characterized by some properties and background knowledge expressed by taxonomies, similarity measures, and affinities between some values. With all such data, the idea is to discover a set of classes, which are described by modal synthesis objects, built up by assertions of high affinity. We use a symbolic clustering algorithm that provides a solution allowing for convergence towards a local optimum for a given criterion and a generalization algorithm to build modal synthesis objects. We give finally an example to illustrate this method: the advising of the University of Algiers students.
