The structural information of data contains useful prior knowledge and thus is important for designing classifiers. Extreme learning machine (ELM) has been a potential technique in handling classification problems. However, it only simply considers the prior class-based structural information and ignores the prior knowledge from statistics and geometry of data. In this paper, to capture more structural information of the data, we first propose a Fisher-regularized extreme learning machine (called Fisher-ELM) by applying Fisher regularization into the ELM learning framework, the main goals of which is to build an optimal hyperplane such that the output weight and within-class scatter are minimized simultaneously. The proposed Fisher-ELM reflects both the global characteristics and local properties of samples. Intuitively, the Fisher-ELM can approximatively fulfill the Fisher criterion and can obtain good statistical separability. Then, we exploit graph structural formulation to obtain semi-supervised Fisher-ELM version (called Lap-FisherELM) by introducing manifold regularization that characterizes the geometric information of the marginal distribution embedded in unlabeled samples. An efficient successive overrelaxation algorithm is used to solve the proposed Fisher-ELM and Lap-FisherELM, which converges linearly to a solution, and can process very large datasets that need not reside in memory. The proposed Fisher-ELM and Lap-FisherELM do not need to deal with the extra matrix and burden the computations related to the variable switching, which makes them more suitable for relatively large-scale problems. Experiments on several datasets verify the effectiveness of the proposed methods.

数据的结构信息包含有用的先验知识，因此对于设计分类器很重要。极限学习机（ELM）已成为处理分类问题的潜在技术。但是，它仅考虑了基于先验类的结构信息，而忽略了统计数据和数据几何中的先验知识。在本文中，为了捕获数据的更多结构信息，我们首先通过将Fisher正则化应用到ELM学习框架中，提出了Fisher正规化的极限学习机（称为Fisher-ELM），其主要目标是构建最优的超平面从而使输出重量和类别内分散同时最小化。提出的Fisher-ELM既反映了样品的整体特性又反映了其局部特性。凭直觉 Fisher-ELM可以近似满足Fisher标准，并且可以获得良好的统计可分离性。然后，通过引入流形正则化来表征嵌入在未标记样本中的边际分布的几何信息，我们利用图结构公式来获得半监督的Fisher-ELM版本（称为Lap-FisherELM）。使用有效的连续超松弛算法来解决所提出的Fisher-ELM和Lap-FisherELM，它们线性收敛到一个解决方案，并且可以处理不需要驻留在内存中的非常大的数据集。提出的Fisher-ELM和Lap-FisherELM不需要处理额外的矩阵，也不必负担与变量切换相关的计算，这使它们更适合于相对较大的问题。