Robust Extreme Learning Machine Based on p-order Laplace Kernel-Induced Loss Function

Abstract

Since the datasets of the practical problems are usually affected by various noises and outliers, the traditional extreme learning machine (ELM) shows low prediction accuracy and significant fluctuation of prediction results when learning such datasets. In order to overcome this shortcoming, the l2 loss function is replaced by the correntropy loss function induced by the p-order Laplace kernel in the traditional ELM. Correntropy is a local similarity measure, which can reduce the impact of outliers in learning. In addition, introducing the p-order into the correntropy loss function is rewarding to bring down the sensitivity of the model to noises and outliers, and selecting the appropriate p can enhance the robustness of the model. An iterative reweighted algorithm is selected to obtain the optimal hidden layer output weight. The outliers are given smaller weights in each iteration, significantly enhancing the robustness of the model. To verify the regression prediction of the proposed model, it is compared with other methods on artificial datasets and eighteen benchmark datasets. Experimental results demonstrate that the proposed method outperforms other methods in the majority of cases.