Faculté des sciences de base SB, Département de mathématiques, Institut de mathématiques IMA (Chaire de recherche opérationnelle SE ROSE)

## The use of Boolean concepts in general classification contexts

### Thèse sciences Ecole polytechnique fédérale de Lausanne EPFL : 2000 ; no 2316.

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Summary
Data classification, in the present context, concerns the use of computers in order to create systems that learn how to automatically decide to which of a predefined set of classes a given object belongs. Boolean concepts have long been present in data classification, and still are today, at various levels. We consider a kind of Boolean elements, called patterns, which consist of specific conjunctions of Boolean facts. Assuming the existence of two classes of objects, the positive and the negative, patterns can be expressed as conditionals of the type "If A and B and not C, then positive", where A, B, and C are Boolean values, each associated with a specific attribute describing the objects to be classified. From the classification system point of view, patterns are basic Boolean expressions that can be processed in a purely mathematical manner. However, if the values of the conjunction have an intuitive meaning, then this type of representation provides an intuitive perspective of the classification system, which can be interpreted by humans. The use of sets of patterns for building classification systems is justified by the fact that certain conjunctions of the type described above are matched by objects of one class but not by those of the other class. In this sense, patterns possess distinguishing properties that can be used to determine whether an object belongs to a class (if it matches certain patterns) or not. In this thesis, we consider the use of classification systems based on patterns, which we have seen to be inherently Boolean, in the context of classification tasks where nothing is Boolean, that is to say, where the objects are described by multi-valued or continuous attributes and instead of a positive/negative decision, suitable to situations where only two classes are involved, the output is rather the selection of a class among several. The work presented here extends along different directions. It starts by the study of a suitable way of transforming the attributes describing the objects to be classified into equivalent Boolean attributes. We describe the constraints that must be satisfied by this transformation and present a procedure allowing it to be done in a short amount of time. Another research direction explores the possibility of generating multi-class divisions with systems whose output is Boolean. This study has the benefit of also being applicable to other types of classification systems adapted to two-class situations, but whose internal language is not necessarily Boolean. This is the case of some current state-of-the-art systems. To realize this adaptation, the common approach consists in decomposing the original problem into several two-class sub-problems and generating an independent classification system to solve each one of them. The final class decision is obtained from the combination of the partial Boolean decisions. We analyze and compare several existing procedures for this purpose, and in addition propose an interesting new procedure. Finally, we consider the possibility of sharing patterns among several classes and develop a Boolean-based classification system which is directly adapted to multi-class problems, but maintaining the property of being understandable by humans. We show that the performance of this type of system is not in all cases comparable to the best available systems, but they have the advantage of providing, in certain circumstances, a better understanding of the problem at hand.