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

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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.

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Notes

  1. TPROD efficiently allows any type of tensor product between two multi-dimensional arrays, which can be downloaded from Mathworks’s file exchange.

  2. TT2-ELM’s source MATLAB code can be download directly from https://github.com/zggl/TriT2ELM.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11771111 and 61603126), and the Natural Science Foundation of Heilongjiang Province with Grant No. QC2016094.

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Authors and Affiliations

  1. School of Science, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Sharina Huang & Minghao Chen

  2. College of Electronic Information Engineering, Inner Mongolia University, Hohhot, 010021, People’s Republic of China

    Guoliang Zhao

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  1. Sharina Huang
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  2. Guoliang Zhao
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  3. Minghao Chen
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Correspondence to Sharina Huang.

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Huang, S., Zhao, G. & Chen, M. Tensor extreme learning design via generalized Moore–Penrose inverse and triangular type-2 fuzzy sets. Neural Comput & Applic 31, 5641–5651 (2019). https://doi.org/10.1007/s00521-018-3385-5

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