L1-Norm Robust Regularized Extreme Learning Machine with Asymmetric C-Loss for Regression

Extreme learning machines (ELMs) have recently attracted significant attention due to their fast training speeds and good prediction effect. However, ELMs ignore the inherent distribution of the original samples, and they are prone to overfitting, which fails at achieving good generalization performance. In this paper, based on expectile penalty and correntropy, an asymmetric C-loss function (called AC-loss) is proposed, which is non-convex, bounded, and relatively insensitive to noise. Further, a novel extreme learning machine called L-1 norm robust regularized extreme learning machine with asymmetric C-loss (L-1-ACELM) is presented to handle the overfitting problem. The proposed algorithm benefits from L-1 norm and replaces the square loss function with the AC-loss function. The L-1-ACELM can generate a more compact network with fewer hidden nodes and reduce the impact of noise. To evaluate the effectiveness of the proposed algorithm on noisy datasets, different levels of noise are added in numerical experiments. The results for different types of artificial and benchmark datasets demonstrate that L-1-ACELM achieves better generalization performance compared to other state-of-the-art algorithms, especially when noise exists in the datasets.