Deep Neural-Fuzzy System Algorithms with Improved Interpretability for Classification Problems

Yunhu Huang, Geng Lin, De-wang Chen, Wendi Zhao

Abstract: The adaptive neuro-fuzzy inference system (ANFIS), an efficient soft computing approach, has both high interpretability and self-learning ability. ANFIS can effectively handle the both classification and regression of low-dimensional data, but it deals poorly with high-dimensional big data due to the curse of dimensionality. This paper proposes a highly interpretable deep neural-fuzzy system (DNFSA)-based algorithm to efficiently and effectively train fuzzy classifiers. It integrates several novel techniques: (1) independent membership functions (MFs) and fuzzy c-means clustering, which initialize rule by fuzzy c-means clustering to train Takagi–Sugeno–Kang fuzzy system efficiently and (2) maximal information coefficient, which identifies interesting relationships between pairs of variables, so as to enhance the interpretability and generalization performance. Specifically, by viewing improved ANFIS as the base learner, we construct DNFSA in the fashion of parallel layer by layer. A visualized structure can be obtained automatically and presented to the users for better understanding of DNFSA. Furthermore, the proposed DNFSA can effectively determine which base learners should be abandoned from a set of available sub-fuzzy systems, which reveals that it may be better to ensemble many sub-fuzzy systems instead of all at hand. Experiments are conducted to confirm the DNFSA can significantly reduce the rules along with the parameters to have better interpretability.