Characterization of Symbolic Rules Embedded in Deep DIMLP Networks: A Challenge to Transparency of Deep Learning

Rule extraction from neural networks is a fervent research topic. In the last 20 years many authors presented a number of techniques showing how to extract symbolic rules from Multi Layer Perceptrons (MLPs). Nevertheless, very few were related to ensembles of neural networks and even less for networks trained by deep learning. On several datasets we performed rule extraction from ensembles of Discretized Interpretable Multi Layer Perceptrons (DIMLP), and DIMLPs trained by deep learning. The results obtained on the Thyroid dataset and the Wisconsin Breast Cancer dataset show that the predictive accuracy of the extracted rules compare very favorably with respect to state of the art results. Finally, in the last classification problem on digit recognition, generated rules from the MNIST dataset can be viewed as discriminatory features in particular digit areas. Qualitatively, with respect to rule complexity in terms of number of generated rules and number of antecedents per rule, deep DIMLPs and DIMLPs trained by arcing give similar results on a binary classification problem involving digits 5 and 8. On the whole MNIST problem we showed that it is possible to determine the feature detectors created by neural networks and also that the complexity of the extracted rulesets can be well balanced between accuracy and interpretability.

LEARNING DECISION REGIONS BASED ON ADAPTIVE ELLIPSOIDS

A fuzzy classifier using multiple ellipsoids to approximate decision regions for classification is designed in this paper. To learn the sizes and orientations of ellipsoids, an algorithm called evolutionary ellipsoidal classification algorithm (EECA) that integrates the genetic algorithm (GA) with the Gustafson-Kessel algorithm (GKA) is proposed. Within EECA the GA is employed to learn the size of every ellipsoid. With the size of every ellipsoid encoded and intelligently estimated in the GA chromosome, GKA is utilized to learn the corresponding ellipsoid. GKA is able to adapt the distance norm to the underlying distribution of the prototype data points for an assigned ellipsoid size. A process called directed initialization is proposed to improve EECA's learning efficiency. Because EECA learns the data point distribution in every cluster by adjusting an ellipsoid with suitable size and orientation, the information contained in the ellipsoid is further utilized to improve the cluster validity. A cluster validity measure based on the ratio of summation for each intra-cluster scatter with respect to the inter-cluster separation is defined in this paper. The proposed cluster validity measure takes advantage of EECA's learning capability and serves as an effective index for determining the adequate number of ellipsoids required for classification.