Stacked Ensemble of Extremely Interpretable Takagi-Sugeno–Kang Fuzzy Classifiers for High-Dimensional Data

Abstract

To overcome the inappropriateness of the recently-developed fully interpretable Takagi-Sugeno–Kang fuzzy systems (FIMG-TSK) for high-dimensional classification tasks, which is caused by their unreliable Gaussian mixture models and their very lengthy fuzzy rules on all the original features, this study attempts to develop a stacked ensemble of extremely interpretable first-order TSK fuzzy classifiers (SEXI-TSK-FC) comprising extremely interpretable FIMG-TSK-based classifiers. SEXI-TSK-FC has structural and algorithmic novelties. In the structural sense, to guarantee enhanced generalizability and short fuzzy rules, the proposed XI-TSK is created as each subclassifier on a subset of the original features. Then it stacks each successive subclassifier on both the outputs and the important features selected, which are from the incorrectly classified dataset by the previous subclassifier. After that, SEXI-TSK-FC linearly aggregates all the outputs of its subclassifiers with a one-step calculation to enhance classification accuracy while preserving extreme interpretability. In the algorithmic sense, each short fuzzy rule of the XI-TSK subclassifier is determined using the proposed fuzzy feature selection and clustering algorithm to select the subset of all the original features and simultaneously fix the antecedent and consequent of each rule. After that, the rule weights in each subclassifier are trained quickly with strong generalizability using the proposed Vapnik-Chervonenkis dimension minimization-based learning. Experimental results on 12 benchmark datasets demonstrate the power of the proposed classifier SEXI-TSK-FC on high-dimensional data in testing accuracy, training time, and extreme interpretability.