Journal
NEUROCOMPUTING
Volume 74, Issue 16, Pages 2475-2482Publisher
ELSEVIER
DOI: 10.1016/j.neucom.2010.12.037
Keywords
Extreme learning machine; Regression; Optimization; Matrix theory
Categories
Funding
- National Natural Science Foundation [90818020, 60873206, 61001200]
- Natural Science Foundation and Education Department of Zhejiang [Y7080235, Y6100010]
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Extreme learning machine (ELM) is one of the most popular and important learning algorithms. It comes from single-hidden-layer feedforward neural networks. It has been proved that ELM can achieve better performance than support vector machine (SVM) in regression and classification. In this paper, mathematically, with regression problem, the step 3 of ELM is studied. First of all, the equation H beta=T are reformulated as an optimal model. With the optimality, the necessary conditions of optimal solution are presented. The equation H beta=T is replaced by (HH)-H-T beta= (HT)-T-T. We can prove that the latter must have one solution at least. Second, optimal approximation solution is discussed in cases of H is column full rank, row full rank, neither column nor row full rank. In the last case, the rank-1 and rank-2 methods are used to get optimal approximation solution. In theory, this paper present a better algorithm for ELM. (C) 2011 Elsevier B.V. All rights reserved.
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