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Extreme learning machine with feature mapping of kernel function

Kernel-based extreme learning machine (KELM) solves the problem of random initialisation of extreme learning machine (ELM), and it has a faster learning speed and higher learning accuracy. However, when it comes to a scenario in which the dimensionality of kernel function mapping space is less than the number of samples, the kernel function theoretically cannot be introduced into ELM. To solve this problem, ELM with feature mapping (FM) of kernel function (FM-KELM) is proposed in this study, in which the random FM between the input layer and hidden layer of ELM is replaced with the FM of the kernel function. Moreover, the authors prove that when the regularised parameter C is close to zero, the solution of introduced kernel function is approximately equal to the correct solution. The proposed algorithm is more robust than KELM for the parameter C. Several experimental results show that the proposed algorithm in this study achieves higher classification accuracy without excessive parameter tuning, and the duration of the training and testing process is significantly reduced.