基于截断1-范数损失函数的鲁棒超限学习机

对噪声和异常值较敏感、鲁棒性差是超限学习机（ELM）的主要问题.在1-范数损失函数的基础上，提出截断1-范数损失函数来抑制噪声和异常值的影响，建立了基于截断1-范数损失函数的鲁棒ELM模型.通过迭代重赋权算法求解对应的优化问题，并利用4个模拟数据集和9个真实数据集验证模型的有效性.数值实验结果表明，在噪声环境下鲁棒ELM的泛化性能优于对比方法，并且具有较强的鲁棒性，尤其是在异常值比例较大的情形下.

Robust ELM model with truncated 1-norm loss function

Sensitivity to noises and outliers and inferior robustness are the primary problems associated with extreme learning machine(ELM).Based on the 1-norm loss function,a truncated 1-norm loss function is proposed to suppress the effects of noises and outliers.A robust ELM model with truncated 1-norm loss function is established.The corresponding optimization problem is solved by iterative re-weighted algorithm.Four simulated data sets and nine real-world data sets are used to verify the validity of the proposed model.The numerical results show that the generalization performance of robust ELM in noisy environment is superior to that of the compared methods and has superior robustness,especially in the case of a substantial proportion of outliers.