基于微分同胚的鲁棒激活函数的极端学习机

极端学习机作为一种分类算法已被广泛应用于各个领域，并取得较好的效果。然而在实际问题中数据的不规则分布、带有噪音以及离群点，都严重影响了极端学习机算法的分类准确率。针对这些问题，深入分析不同激活函数的特性，提出了一种基于角度优化和微分同胚理论的鲁棒激活函数（Robust activation function）。该鲁棒激活函数通过角度优化及微分同胚揭示数据的内在流形，从理论上证明了中心化样本长度与其偏离主空间角度为子空间偏离的主要因素，进而解决了噪音造成的主空间偏离问题，并且可尽量避免激活函数的输出值趋于零的情况。实验结果表明本文提出的激活函数优于其他的激活函数。

Robust activation function of extreme learning machine based on differential homeomorphism

As a classification algorithm ,Extreme learning machine,has been widely used in the every area and got good result. But in practical application, the irregular distribution of the data,with noise and outliers, seriously affect the classification accuracy of the extreme learning machine .Aiming at those problems,making a deep analysis in the characteristics of different activation functions,a Robust activation function is presented based on the angle of optimization and differential homeomorphism theory (Robust activation function). The robust activation function reveals internal manifold of the data by optimizing the angle and differential homeomorphism and theoretically proves that the major factor of the subspace deviation is the length of centralized sample and its deviation angle from main space.Then it solves the noise caused by the deviation from the main space problem and proposes that the activation function can avoid the output value of the activation function tending to zero.Experimental results show that the proposed activation function is superior to other activation function.