Fisher-regularized supervised and semi-supervised extreme learning machine

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.