This paper presents theoretical and historical backgrounds related to neural network rule extraction. It also investigates approaches for neural network rule extraction by ensemble concepts. Bologna pointed out that although many authors had generated comprehensive models from individual networks, much less work had been done to explain ensembles of neural networks. This paper carefully surveyed the previous work on rule extraction from neural network ensembles since 1988. We are aware of three major research groups i.e., Bologna' group, Zhou' group and Hayashi' group. The reason of these situations is obvious. Since the structures of previous neural network ensembles were quite complicated, the research on the efficient rule extraction algorithm from neural network ensembles was few although their learning capability was extremely high. Thus, these issues make rule extraction algorithm for neural network ensemble difficult task. However, there is a practical need for new ideas for neural network ensembles in order to realize the extremely high-performance needs of various rule extraction problems in real life. This paper successively explain nature of artificial neural networks, origin of neural network rule extraction, incorporating fuzziness in neural network rule extraction, theoretical foundation of neural network rule extraction, computational complexity of neural network rule extraction, neuro-fuzzy hybridization, previous rule extraction from neural network ensembles and difficulties of previous neural network ensembles. Next, this paper address three principles of proposed neural network rule extraction: to increase recognition rates, to extract rules from neural network ensembles, and to minimize the use of computing resources. We also propose an ensemble-recursive-rule extraction (E-Re-RX) by two or three standard backpropagation to train multi-layer perceptrons (MLPs), which enabled extremely high recognition accuracy and the extraction of comprehensible rules. Furthermore, this enabled rule extraction that resulted in fewer rules than those in previously proposed methods. This paper summarizes experimental results of rule extraction using E-Re-RX by multiple standard backpropagation MLPs and provides deep discussions. The results make it possible for the output from a neural network ensemble to be in the form of rules, thus open the "black box" of trained neural networks ensembles. Finally, we provide valuable conclusions and as future work, three open questions on the E-Re-RX algorithm.
Designing a decompositional rule extraction algorithm for neural networks with bound decomposition tree
