A Boolean Algebra Based Rule Extraction Algorithm for Neural Networks with Binary or Bipolar Inputs

Neural networks have been applied in various domain including science, commerce, medicine, and industry. However, The knowledge learned by a trained neural network is difficult to understand. This paper proposes a Boolean algebra based algorithm to extract comprehensible Boolean rules from supervised feed-forward neural networks to uncover the black-boxed knowledge. This algorithm is called the BAB-BB rule extraction algorithm, which stands for a Boolean algebra based rule extraction algorithm for neural networks with binary and bipolar inputs. Decomposition techniques and interval arithmetic are used in the algorithm. First, each neuron associated with its inputs is analyzed and a Boolean function, describing the activation rule from its inputs to the neuron, is derived. These Boolean functions are merged into an aggregated Boolean rule according to the network topology. The Boolean rule is then further simplified by Boolean algebra operations. During the rule extraction procedure, redundant hidden neurons can be detected and removed without affecting the original function of the neural network. Examples of unipolar and bipolar inputs are presented to demonstrate the use of our algorithm. Finally, the Exclusive OR problem is presented and solved by our algorithm. Results show that our BAB-BB algorithm is practicable and of high efficiency.