Tensor extreme learning design via generalized Moore–Penrose inverse and triangular type-2 fuzzy sets

Abstract

A tensor-based extreme learning machine is proposed, which is referred to as tensor-based type-2 extreme learning machine (TT2-ELM). In contrast to the work on ELM, regularized ELM (RELM), weighted regularized ELM (WRELM) and least squares support vector machine (LS-SVM), which are the most often used learning algorithm in regression problems, TT2-ELM adopts the tensor structure to construct the ELM for type-2 fuzzy sets, Moore–Penrose inverse of tensor is used to obtain the tensor regression result. No further type-reduction method is needed to obtain the coincide type-1 fuzzy sets, and type-2 fuzzy structure can be seamlessly incorporated into the ELM scheme. Experimental results are carried out on two Sinc functions, a nonlinear system identification problem and four real-world regression problems, results show that TT2-ELM performs at competitive level of generalized performance as the ELM, RELM, WRELM and LS-SVM on the small- and moderate-scale data sets.