This paper concerns estimation of generalization performance of the multi-output extreme learning machine classifier (M-ELM) in the framework of statistical learning theory. The performance bound is derived under the assumption that the expectation of the extreme learning machine kernel exists. We first show that minimizing the least square error is equal to minimizing an upper bound of the error concerning the margin of M-ELM in the training set, which implies that M-ELM ends up with high confidence after training. Afterwards, we derive the bound based on the margin of M-ELM and the empirical Rademacher complexity. The bound not only gives a theoretical explanation of good performance of M-ELM especially in the small-sample cases, but also shows that the performance of M-ELM is insensitive to the number of hidden nodes, which is consistent with previous experimental results. The bound also offers an insight that the performance of M-ELM is not significantly affected by the number of classes, which proves the effectiveness of the learning process of M-ELM.

中文翻译：

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多输出极限学习机分类器的性能界限

本文涉及在统计学习理论框架下对多输出极限学习机分类器（M-ELM）的泛化性能的估计。性能界限是在假设存在极限学习机内核的前提下得出的。我们首先显示最小化最小平方误差等于最小化关于训练集中M-ELM余量的误差上限，这意味着M-ELM在训练后最终具有高置信度。然后，我们基于M-ELM的余量和经验Rademacher复杂度得出边界。该界限不仅为M-ELM的良好性能提供了理论上的解释，尤其是在小样本情况下，还表明M-ELM的性能对隐藏节点的数量不敏感，这与以前的实验结果一致。该界限还提供了一种见解，即M-ELM的性能不受班级数量的显着影响，这证明了M-ELM的学习过程的有效性。