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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, seriously. To improve the robustness of KELM, this article proposes a mixture correntropy-based KELM (MC-KELM), which adopts the recently proposed maximum mixture correntropy criterion as the optimization criterion, instead of using the MMSE criterion. In addition, an online sequential version of MC-KELM (MCOS-KELM) is developed to deal with the case that the data arrive sequentially (one-by-one or chunk-by-chunk). Experimental results on regression and classification data sets are reported to validate the performance superiorities of the new methods. [ABSTRACT FROM AUTHOR]

Random Fourier adaptive filters (RFAFs) project the original data into a high-dimensional random Fourier feature space (RFFS) such that the network structure of filters is fixed while achieving similar performance with kernel adaptive filters. The commonly used error criterion in RFAFs is the well-known minimum mean-square error (MMSE) criterion, which is optimal only under the Gaussian noise assumption. However, the MMSE criterion suffers from instability and performance deterioration in the presence of non-Gaussian noises. To improve the robustness of RFAFs against large outliers, the maximum correntropy criterion (MCC) is applied to RFFS, generating a novel robust random Fourier filter under maximum correntropy (RFFMC). To further improve the filtering accuracy, a random-batch RFFMC (RB-RFFMC) is also presented. In addition, a theoretical analysis on the convergence characteristics and steady-state excess mean-square error of RFFMC and RB-RFFMC is provided to validate their superior performance. Simulation results illustrate that RFFMC and its extension provide desirable filtering performance from the aspects of filtering accuracy and robustness, especially in the presence of impulsive noises. [ABSTRACT FROM AUTHOR]