Adaptive Laplacian Support Vector Machine for Semi-supervised Learning

Laplacian support vector machine (LapSVM) is an extremely popular classification method and relies on a small number of labels and a Laplacian regularization to complete the training of the support vector machine (SVM). However, the training of SVM model and Laplacian matrix construction are usually two independent process. Therefore, In this paper, we propose a new adaptive LapSVM method to realize semi-supervised learning with a primal solution. Specifically, the hinge loss of unlabelled data is considered to maximize the distance between unlabelled samples from different classes and the process of dealing with labelled data are similar to other LapSVM methods. Besides, the proposed method embeds the Laplacian matrix acquisition into the SVM training process to improve the effectiveness of Laplacian matrix and the accuracy of new SVM model. Moreover, a novel optimization algorithm considering primal solver is proposed to our adaptive LapSVM model. Experimental results showed that our method outperformed all comparison methods in terms of different evaluation metrics on both real datasets and synthetic datasets.