Extreme Learning Machine Research And Application Based On (?)1 Norm And Pinball Loss Function

Extreme learning machine(ELM)has been widely used in the field of regression due to their advantages such as fast training speed and ease of implementation.However,the squared loss function of the ELM model is sensitive to outliers,which can easily lead to overfitting of the model.To address the deficiency of robustness of ELM,this paper proposes an ELM based on the Capped (?)11 norm with a Pinball loss function and an ELM based on the asymmetric ε-insensitive Pinball loss function,as follows:The Pinball loss function is linearly correlated with the error,which reduces the effect of outliers compared to the squared loss function.Meanwhile,Capped (?)11 norm regularization is introduced into the objective function to reduce the complexity of the ELM model.In this paper,we propose an ELM based on Capped (?)11 norm regularization and Pinball loss function,which uses an iterative reweighting algorithm to minimize the objective function.During the iterative process,the Pinball loss function parameter p is controlled,and the outliers are given smaller weights according to the principle of larger errors and smaller weights.In addition,adjusting the parameter u of the Capped (?)11 norm regularization can better improve the model generalization performance.The model achieves optimality in 41 out of 54 experimental results for 18 datasets,and the proposed model shows good robustness as the proportion of outliers increases.The asymmetric ε-insensitive Pinball loss function is linearly correlated with the error outside the insensitive region,and the impact of outliers is reduced by controlling the error growth rate through the selection of parameter τ.In this paper,we propose an ELM based on the asymmetric ε-insensitive Pinball loss function and use an iterative reweighting algorithm to solve the corresponding optimization problem.In the iterative process,the training samples falling in the ε-insensitive region are set to a value of 0,and the training samples falling on both sides of the insensitive region are assigned weights according to their errors.The experimental results show that the model is not only insensitive to outliers but also has good generalization and robustness in the presence of a high proportion of outliers.