Knowledge Representation and Symbolic Data Analysis

Summary

The main aim of the symbolic approach in data analysis is to extend problems, methods and algorithms used on classical data to more complex data well adapted to represent knowledge which “unifies” instead of observations which characterize “individual things”: for instance, “the customers of my shop” instead of “a customer of my shop”, a “a kind of mushroom” instead of “the mushroom, that I have in my hand”. In Diday (1987) we have introduced several kinds of symbolic objects (“events”, “assertions”, “hordes” and “synthesis objects”) which describe them. We extend these to “symbolic objects of classes” whose extension are classes instead of individuals and to “modal symbolic objects” by using, as in modal logic, operators called “modes” which change the meaning of logic formula. We show that properties and qualities of symbolic objects given in Diday (1988) and Brito and Diday (1990) may be extended to these objects. As pointed out in Diday (1988), symbolic objects may be used to describe clusters obtained after a clustering or factors after a factorial analysis in a more explanatory way for the user than the usual center of gravity or a linear combination of the variables. We define a family of symbolic data analysis problems. Some general principles concerning the algorithms which yield solutions to these problems are given and illustrated by a simple example using modal symbolic assertion of classes.