Batch kernel neuro-fuzzy system ensemble framework with residual learning and selection mechanism

Takagi-Sugeno-Kang (TSK) fuzzy systems are powerful modeling approaches. When modeling real-world data, they face limitations in terms of computing efficiency and modeling accuracy. This paper designs a batch kernel neuro-fuzzy system ensemble (BKNFSE) framework to overcome these issues, where BKNFSE integrates several batch kernel neuro-fuzzy system (BKNFS) models. From the implementation perspective, the TSK fuzzy system is adopted to generate rules in the fuzzy inference layer of BKNFS, and a combination kernel mapping is designed to capture nonlinear features from fuzzy representations. This manipulation contributes to performance improvements with the fixed number of kernel mapping nodes. To reduce the computational complexity, a batch learning strategy is designed to train the parameters of BKNFS. During batch learning, updated model information is stored in two intermediate matrices, which are utilized to update the output weight of BKNFS. Subsequently, an ensemble learning framework with a selection mechanism is designed to achieve aggregated modeling performance based on the residual learning strategy. The designed selection mechanism is used to choose BKNFS models for BKNFSE. The results of comprehensive experiments indicate that BKNFSE achieves superior modeling accuracy and training efficiency.