Twin extreme learning machine (TELM) has attracted considerable attention and achieved great success in the machine learning field. However, its performance will be severely affected when outliers exist in the dataset since TELM does not consider heteroscedasticity in practical applications. To improve the performance of TELM, a novel learning framework called twin parametric-margin extreme learning machine (TPMELM) was proposed. Further, to enhance the classification performance of our TPMELM in a semi-supervised learning setting, a Laplacian TPMELM (Lap-TPMELM) was developed by introducing manifold regularization into TPMELM. Using the geometric information of the marginal distribution embedded in unlabeled samples, Lap-TPMELM can effectively construct a more reasonable classifier. The TPMELM and Lap-TPMELM are suitable for many situations, especially when the data has heteroscedastic error structure. Moreover, the TPMELM and Lap-TPMELM are helpful in clarifying theoretical interpretation of parameters which control the bounds on proportions of support vectors and boundary errors. An efficient technique (successive over-relaxation, SOR) is applied in TPMELM and Lap-TPMELM, respectively. Experimental results show the effectiveness and reliability of the proposed methods.

中文翻译：

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有监督和半监督的双参数余量正则化极限学习机

双胞胎极限学习机（TELM）在机器学习领域引起了极大的关注并取得了巨大的成功。但是，当数据集中存在异常值时，其性能将受到严重影响，因为TELM在实际应用中不考虑异方差性。为了提高TELM的性能，提出了一种新型的学习框架，称为双参数极限极限学习机（TPMELM）。此外，为了提高我们的TPMELM在半监督学习环境中的分类性能，通过将流形正则化引入TPMELM中来开发拉普拉斯TPMELM（Lap-TPMELM）。利用嵌入在未标记样本中的边际分布的几何信息，Lap-TPMELM可以有效地构建更合理的分类器。TPMELM和Lap-TPMELM适用于许多情况，特别是当数据具有异方差错误结构时。此外，TPMELM和Lap-TPMELM有助于阐明控制支撑向量比例边界和边界误差的参数的理论解释。TPMELM和Lap-TPMELM中分别应用了一种有效的技术（连续超松弛，SOR）。实验结果表明了所提方法的有效性和可靠性。