Extracting both MofN rules and if-then rules from the training neural networks Norbert Tsopze 1 3 4 - Engelbert Mephu Nguifo 0 2 4 - Gilbert Tindo 3 4 CNRS, UMR 6158, LIMOS , F-63173 Aubie ́re , France CRIL-CNRS UMR 8188, Universite ́ Lille-Nord de France , Artois, SP 16, F-62307 Lens , France Clermont Universite ́, Universite ́ Blaise Pascal , LIMOS, BP 10448, F-63000 Clermont-Ferrand , France Department of Computer Science - Faculty of Science - University of Yaounde I , Cameroon MaxSubsets Generators

a d h3 Trained Artificial Neural Network [Tsopze et al., 2011] N. Tsopze, E. Mephu Nguifo, and G. Tindo. Towards a generalization of decompositional approach of rules extraction from network. In Proceeding IJCNN'11 international joint conference on Neural Networks, 2011.

 Introduction

The general form of a MofN rule is ’if m1 of N1 ^ m2 of N2^:::^mp of Np then conclusion’ or ’Vi(mi of Ni) then conclusion’; for each subset Ni of the inputs set, if mi elements are verified, the conclusion is true.

The common limit of previous approaches is the exclusive form of the extracted rules. Thus we introduce a novel approach called MaxSubset from which it is possible to generate both forms of rules. The MaxSubset approach follows operations (3), (4) and (5) of figure 1; while the existing known algorithms follow the path (1) for the if-then rules and (2) for the MofN rules. The processes (3), (4) and (5) of the figure 1 are described as follows: (3) MaxSubsets and generators extraction; (4) generation of if-then rules from the MaxSubsets (1) (4) h2 c1 c2 c3 (3) (2) (5) (1)ANN to the If the n rules (2) ANN to the MofN rules (3) ANN to the MaxSubsets and the geneartors lsts (4)From the MaxSubsets to the if the rules (5) From the Generators to the MofN rules If - then rules MofN rules list and (5) generation of MofN rules from the generators list. An extended version of this work is described in [Tsopze et al., 2011]. 3

 Conclusion

This approach consists in extracting a minimal list of elements called MaxSubset list, and then generating rules in one of the standard forms : if-then or MofN. To our knowledge, it is the first approach which is able to propose to the user a generic representation of rules from which it is possible to derive both forms of rules.

 Acknowledgments

This work is partially supported by the French Embassy in Cameroon, under the first author’s PhD grant provided by the French Embassy Service SCAC (Service de Coope´ration et d’Action Culturelle). [Andrews et al., 1995] R. Andrews, J. Diederich, and A. Tickle. Survey and critique of techniques for extracting rules from trained artificial neural networkss. KnowledgeBased Systems, 8(6):373–389, 1995.