Robust extreme learning fuzzy systems using ridge regression for small and noisy datasets

Fuzzy Extreme Learning Machine (F-ELM) constructs a fuzzy neural networks by embedding fuzzy membership functions and rules into the hidden layer of extreme learning machine (ELM), that is, it can be interpreted as a fuzzy system with the structure of neural network. Although F-ELM has shown the characteristics of fast learning of model parameters, it has poor robustness to small and noisy datasets since its parameters connecting hidden layer with output layer are optimized by least square(LS). In order to overcome this challenge, a Ridge Regression based Extreme Learning Fuzzy System (RR-EL-FS) is presented in this study, which has introduced the strategy of ridge regression into F-ELM to enhance the robustness. The experimental results also validate that the performance of RR-EL-FS is better than F-ELM and some related methods to small and noisy datasets.