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Kernel-based extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has achieved outstanding performance in addressing various regression and classification problems. Compared with the basic ELM, KELM has a better generalization ability owing to no needs of the number of hidden nodes given beforehand and random projection mechanism. Since KELM is derived under the minimum mean square error (MMSE) criterion for the Gaussian assumption of noise, its performance may deteriorate under the non-Gaussian cases, seriou