Deep Neural Fuzzy System Oriented toward High-Dimensional Data and Interpretable Artificial Intelligence

Fuzzy systems (FSs) are popular and interpretable machine learning methods, represented by the adaptive neuro-fuzzy inference system (ANFIS). However, they have difficulty dealing with high-dimensional data due to the curse of dimensionality. To effectively handle high-dimensional data and ensure optimal performance, this paper presents a deep neural fuzzy system (DNFS) based on the subtractive clustering-based ANFIS (SC-ANFIS). Inspired by deep learning, the SC-ANFIS is proposed and adopted as a submodule to construct the DNFS in a bottom-up way. Through the ensemble learning and hierarchical learning of submodules, DNFS can not only achieve faster convergence, but also complete the computation in a reasonable time with high accuracy and interpretability. By adjusting the deep structure and the parameters of the DNFS, the performance can be improved further. This paper also performed a profound study of the structure and the combination of the submodule inputs for the DNFS. Experimental results on five regression datasets with various dimensionality demonstrated that the proposed DNFS can not only solve the curse of dimensionality, but also achieve higher accuracy, less complexity, and better interpretability than previous FSs. The superiority of the DNFS is also validated over other recent algorithms especially when the dimensionality of the data is higher. Furthermore, the DNFS built with five inputs for each submodule and two inputs shared between adjacent submodules had the best performance. The performance of the DNFS can be improved by distributing the features with high correlation with the output to each submodule. Given the results of the current study, it is expected that the DNFS will be used to solve general high-dimensional regression problems efficiently with high accuracy and better interpretability.