A novel adversarial deep TSK fuzzy classifier with its inverse-free fast training

Deep learning is one of the most popular machine learning methods, and has been used in many applications. However, conventional deep learning is a fully deterministic model that has difficulty reducing data uncertainty while shedding no light on model transparency. To this end, a novel adversarial deep Takagi–Sugeno–Kang (TSK) fuzzy classifier (AD-TSK), which is characterized by its novel stacked structure and inverse-free fast training, is proposed in this paper. After taking the TSK fuzzy classifier as the subclassifier in each layer of AD-TSK, proactive adversarial example learning is designed based on the adversarial attacks on both the features and labels of the inputs for each subclassifier to generate the adversarial TSK fuzzy classifier (ATSK) with increased robustness to noise. Moreover, the generalization capability of AD-TSK can be guaranteed by its novel stacked structure constructed using the dropout-based gradients of each ATSK to update the original inputs along the stacked structure in a layer-by-layer manner. In particular, by sharing the merits of the Schur complement and Sherman–Morrison formula, the consequent parameters of all fuzzy rules in each ATSK can be determined without the matrix inversion operation, and the corresponding optimal number of fuzzy rules can be optimized based on the previous consequent parameters of all fuzzy rules. This can facilitate the inverse-free fast deep learning algorithm of AD-TSK while maintaining interpretability. Extensive experiments on fourteen benchmark datasets from the UCI and KEEL data repositories and the corresponding statistical test results demonstrate the effectiveness of the proposed AD-TSK as well as its inverse-free fast training. The source code of AD-TSK classifier can be downloaded from https://github.com/gusuhang10/AD-TSK .