Fuzzy wavelet extreme learning machine

Incorporating the time-frequency localization properties of wavelets and the learning abilities of neural network (NN), the approximate reasoning characteristics of fuzzy inference system and the advantages of ELM (one-pass learning and good generalization performance at extremely fast learning speed) can exhibit their characteristics to reveal an effective solution in many applications. Following that, this paper presents a novel structure called fuzzy wavelet extreme learning machine (FW-ELM). The main objectives of FW-ELM are to significantly reduce the network complexity by reducing the number of linear learning parameters, and to decrease the sensitivity to random initialization procedure while the acceptable accuracy and generalization performances are preserved. In the proposed structure, each fuzzy rule corresponds to a sub-wavelet neural network and consists of wavelets with different dilations and translations. In this model, in order to achieve a balance between network complexity and performance accuracy, in the THEN-part of each fuzzy rule, one coefficient is considered for each two inputs. In this work, first, the equivalence of an FW model and an SLFN is proved and then ELM can be directly applied to the model. All free parameters of membership functions and wavelet coefficients are generated randomly, and only the output weights are determined analytically using a one-pass learning method. To evaluate FW-ELM, it is compared with popular fuzzy models like OS-Fuzzy-ELM, Simpl_eTS, ANFIS and several other relevant algorithms such as ELM, BP and SVR on various benchmark datasets. Simulation results demonstrate the remarkable efficiency resulting from the proposed approach. Performance accuracy of FW-ELM is shown to be comparable with OS-Fuzzy-ELM and better than the rest of the well-known methods.