Approximate Order Of Approximate Incremental Extreme Learning Machine

Convex incremental extreme learning machine (CI-ELM) is an improved incremental extreme learning machine(I-ELM), use Barron’s convex optimiza-tion method recalled the output weights of the existing hidden nodes when a new hidden node is added. It has been proved that CI-ELM can converge to any continuous function as long as the hidden activation functions are nonlinear piecewise continuous. However, there has been few study on the fast learning essence of CI-ELM in theory. In this thesis, we focus on analyzing the approx-imation capability of CI-ELM from the quantitative point of view. The main results are presented as follows:Chapter 1 systematically introduces the background and development of artificial neural networks (ANNs) and extreme learning machine ELM algorithm.Chapter 2 first gives a brief overview of random mechanisms for function ap-proximation and generalization ability of neural network. Then some background knowledge of I-ELM, including the mathematical preliminaries, the design and procedure of basic I-ELM.Chapter 3 prove the approximation order of CI-ELM based on the con-ditions selection, Meanwhile, numerical experiments validate the feasibility and validity of the obtained results.Chapter 4 Evaluates the approximation order of inequality to further anal-ysis CI-ELM bared on the Cauchy-Schwarz approximation.