INTERPRETABILITY OF RANDOMIZED NEURO-FUZZY INFERENCE SYSTEMS

Abstract

The widespread application of machine learning techniques has led to rapidly rising interest in explainable artificial intelligence that can represent the knowledge gained by the network in an understandable manner. Neuro-fuzzy networks naturally have transparency to the working of the network because of the integration of knowledge representation of the fuzzy system to the networks, which is lacking in networks like Artificial Neural Networks (ANN) and Deep Neural Networks (DNN). This transparency does not guarantee the understandability of the neuro-fuzzy networks as most of these networks are precision-driven and can result in a complex network. In this thesis, the aim is to develop a network with learning capability and good interpretability without a significant reduction and with a less computational burden. Among neuro-fuzzy networks, randomized learning based neuro-fuzzy networks are found to be more accurate with less computational burden compared to conventional neuro-fuzzy networks. Extreme Learning ANFIS (ELANFIS) was found to be the most promising network but this network suffered from the curse of dimensionality and poor interpretability. ELANFIS network is based on grid partitioning which generated an extremely large number of rules for problems with large input features. Clustering based input space partitioning will avoid this large generation of rules but may result in membership functions with excessive overlapping that will lead to poor interpretability. To improve the interpretability of ELANFIS network, modified ELANFIS is proposed where sub-clustering based input space partitioning is done and premise parameters are tuned based on distinguishability constraints for two-sided Gaussian membership functions. The consequent parameters are obtained by extreme learning machine technique. The performance comparison of modified ELANFIS with ANFIS and ELANFIS network shows better interpretability is achieved in modified ELANFIS without a reduction in accuracy. For further reduction in network parameters, a novel similarity index for the generalized bell membership function is defined and a novel distinguishability constraint based on the novel similarity index is designed. Sub-clustering based ELANFIS (CELANFIS) network is proposed where the premise parameters are tuned using the novel distinguishability constraints. Performance comparison for classification shows improved interpretability for CELANFIS network without a reduction in accuracy. As interpretability is subjective in nature, a comparison based on interpretability is difficult. A novel interpretability index is defined for the comparison of networks based on interpretability. iii The study is also extended to input space clustering based on fuzzy c-means and k-means algorithms. In fuzzy c-means based ELANFIS (FCMI-ELANFIS) and k-means based ELANFIS (KMELANFIS) networks, the premise parameters are tuned with a modified tuning based on the novel distinguishability constraints. Performance comparison for real-world regression data shows that clustering based interpretable ELANFIS networks achieve good interpretability without a significant reduction in accuracy and with a less computational burden. Novel performance indices are defined to obtain comparison based on the combination of accuracy and interpretability, and combination of complexity of network, accuracy and interpretability. Analysis based on these novel performance indices shows clustering based interpretable ELANFIS have better performance. As interpretable models with good accuracy are obtained using clustering based interpretable ELANFIS, these networks are used to obtain nonlinear auto-regressive with exogenous input (NARX) model for nonlinear systems. As random vector functional links networks have been shown to outperform extreme learning machine, randomization based ANFIS with functional links (RANFIS-FL) is proposed by integrating RVFL to ANFIS. Randomized neuro-fuzzy networks are used to obtain the NARX models where Bayesian optimization is used to obtain the number of lags in the NARX model, and performance was compared with conventional ANFIS networks based on the novel performance indices. Clustering based Interpretable ELANFIS networks are found to have better performance than conventional ANFIS networks and RANFIS-FL networks.