The constrained optimization extreme learning machine based on the hybrid loss function for regression

In training dataset, the extreme learning machines (ELMs) for data regression are sensitive to noise. This deficiency could be partially overcome by the Constrained optimization based ELM for Regression (C-ELM-R) and the low noise could be managed. However, in general, this is not the case in the real world. This paper addresses a significant note of the C-ELM-Rs poor generalization ability while dealing with the large noise. The Constrained optimization ELM for Regression based on Hybrid loss function (HC-ELM-R) is proposed in this paper with the specific end goal to deal with this problem. The l ₁ norm loss function and the l ₂ norm loss function are combined by the Hybrid loss for limiting the negative influence of large noise on the output weights estimation. The HCO-ELM-R's hybrid loss function can improve the tolerance to large noise, hence, it is less sensitive to large noise as compared to the C-ELM-R. To guarantee that the HC-ELM-R is easy to be solved, the proposed hybrid loss function is specially made smooth and differentiable. Finally, for the verification of the performance of the proposed HC-ELM-R the SinC standard testing function and the actual datasets from UCI machine learning repository were used. The results demonstrated that the robustness of the HC-ELM-R on datasets with large noise is higher as compared to the C-ELM-R and the weighted C-ELM-R.