A Laplacian SVM Based Semi-Supervised Classification Using Multi-Local Linear Model

Semi-supervised learning considers a classification problem of learning from both labeled and unlabeled data. This paper proposes a semi-supervised classification method, in which the potential separation boundary is detected and its information is ingeniously incorporated into a Laplacian support vector machine (LapSVM) in both kernel level and graph level. By applying a pseudo-labeling approach, the input space is first divided into several linear separable partitions along the potential separation boundary. A multi-local linear model is then built for the separation boundary, by interpolating multiple local linear models assigned to the local linear separable partitions. The multi-local linear model is further formulated into a linear regression form with a new input vector in the spanned feature space, which contains the information of potential separation boundary. Then the linear parameters are estimated globally by a LapSVM algorithm. Furthermore, the input in the spanned feature space and pseudo labels are used to construct a label guided graph. Numerical experiments on various real-world datasets and visual representation on toy example exhibit the effectiveness of the proposed method.