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

Abstract

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. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.