Laplacian p-norm proximal support vector machine for semi-supervised classification

In classification, semi-supervised learning occurs when a large amount of unlabeled examples is available with only a small number of labeled examples. In this paper, we propose a novel semi-supervised learning methodology which can realize not only classification but also feature selection automatically. In order to control the interplay between labeled and unlabeled examples, the information from the unlabeled examples is used in a form of Laplace regularization. At the same time, an adjustable norm is introduced to control sparsity and the feature selection. We called this methodology Laplacian -norm proximal support vector machine, Lap-PPSVM for shot. The solution of the optimization problem in Lap-PPSVM is obtained by solving a series systems of linear equations (LEs) and the lower bounds of the solution are established which are extremely helpful for feature selection. Experiments carried out on the real-world and synthetic datasets show the feasibility and effectiveness of the proposed method.