Extreme learning machine (ELM) is an emerging machine learning technique for training single hidden layer feedforward networks (SLFNs). During the training phase, ELM model can be created by simultaneously minimizing the modeling errors and norm of the output weights. Usually, squared loss is widely utilized in the objective function of ELMs, which is theoretically optimal for the Gaussian error distribution. However, in practice, data collected from uncertain and heterogeneous environments trivially result in unknown noise, which may be very complex and cannot be described well using any single distribution. In order to tackle this issue, in this paper, a robust ELM (R-ELM) is proposed for improving the modeling capability and robustness with Gaussian and non-Gaussian noise. In R-ELM, a modified objective function is constructed to fit the noise using mixture of Gaussian (MoG) to approximate any continuous distribution. In addition, the corresponding solution for the new objective function is developed based on expectation maximization (EM) algorithm. Comprehensive experiments, both on selected benchmark datasets and real world applications, demonstrate that the proposed R-ELM has better robustness and generalization performance than state-of-the-art machine learning approaches
