A Novel Style Takagi-Sugeno-Kang Fuzzy Classifier With Its Fast Training on Style Data

The classification of style data generally depends on both physical features of data and distinct styles originating from their own homogeneities. As a first attempt, a novel
s
tyle Takagi-Sugeno-Kang (
TSK
) fuzzy classifier called STSK is developed in this study. STSK as an interpretable classifier consists of interpretable fuzzy rules with powerful representation ability on explicit physical features, implicit style features and the proposed style matrix of style data. By separating all features including the implicit style features in the antecedent parts of all fuzzy rules into fixed fuzzy partitions, followed by randomly assigned Gaussian membership functions with interpretable linguistic terms, the interpretable antecedents and hence the interpretable fuzzy rules can be assured for STSK. The training of STSK can be accomplished by solving the designed objective function through iteratively augmenting style features and updating the consequent parameters (including the style matrices) of all fuzzy rules in the form of their analytical solutions. Furthermore, by means of the Sherman-Morrison and Schur complement formulas, a fast learning algorithm F-STSK is derived to speed up the training of STSK to ensure at least comparable classification performance and simultaneously avoid successive yet time-consuming matrix inversion calculations caused by iterative style feature augmentation. Extensive experimental results on benchmark datasets validate the effectiveness of the proposed fuzzy classifier STSK and its fast learning algorithm. Moreover, six case studies about style data demonstrate the superiority of STSK over the comparison methods. The code of this study can be downloaded from
https://github.com/gusuhang10/STSK
.