- Article
28 Pages
Takagi–Sugeno–Kang (TSK) fuzzy classifiers have achieved notable success in pattern recognition and data mining due to their combination of approximation capability and model interpretability. However, existing TSK classifiers predominantly rely on batch training, which becomes impractical in streaming environments characterized by continuous sample arrival, limited memory, and evolving data distributions. To address these challenges, this paper proposes the Online Adaptive TSK (OA-TSK) fuzzy classifier with an incremental–decremental update protocol for non-stationary data streams. First, we develop the Decremental Adaptive TSK Fuzzy Classifier (DA-TSK), whose update procedure applies the Sherman–Morrison formula to a symmetric rank-one downdate, enabling precise sample removal while maintaining exact equivalence to batch least-squares retraining. Building upon DA-TSK and our prior Dynamic Incremental Adaptive TSK Fuzzy Classifier (DIA-TSK), we then propose OA-TSK, which integrates incremental and decremental updates within a sliding-window mechanism to achieve continuous adaptation with bounded memory. The key theoretical contribution is that, in exact arithmetic, OA-TSK produces at every time step the same ridge-regularized least-squares solution as batch retraining on the active window. To further handle severe shifts in the input distribution, which can cause fixed rule centers to become poorly aligned with newly arriving samples, we propose Online Adaptive TSK with Antecedent Reclustering (OA-A-TSK), which incorporates an adaptive antecedent reclustering mechanism. Comprehensive experiments on synthetic and real-world data streams demonstrate that OA-TSK achieves classification accuracy comparable to that of ridge-regularized batch retraining while substantially reducing per-sample computational complexity. An analysis of average ranks shows that OA-TSK and OA-A-TSK rank among the top-performing methods across diverse drift scenarios while preserving the intrinsic interpretability of TSK fuzzy systems.
Symmetry
21 October 2026





