### Extraction of crisp logical rules using constrained backpropagation networks.

Wlodzislaw Duch,
Rafal Adamczak, and Krzysztof Grabczewski.

Department of Informatics,
Nicolaus Copernicus University,

Grudziadzka 5, 87-100 Torun, Poland.
The problem of extraction of crisp logical rules from neural networks trained
with backpropagation algorithm is solved by transforming these networks into
simpler networks performing logical functions. Two constraints are included in
the cost function: regularization term inducing weight decay and additional
term forcing the remaining weights to +/- 1. Networks with minimal number of
connections are created, leading to a small number of crisp logical rules. A
constructive algorithm is proposed, in which rules are generated consecutively
by adding more nodes to the network. Rules that are most general, covering many
training examples, are created first, followed by more specific rules, covering
a few cases only. Generation of new rules is stopped when their application on
the test dataset does not increase the number of correctly classified cases.
Our constructive algorithm applied to the Iris classification problem generates
two rules with three antecedents giving 98.7% accuracy. A single rule for the
mushroom problem leads to 98.52% accuracy while three additional rules allow
for perfect classification. The rules found for the three monk problems
classify all the examples correctly.

International Joint Conference on Artificial Neural Networks (IJCNN'97), Houston, 9-12.6.1997, pp. 2384-2389

Paper in PDF format, 196KB

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