Novel Class of Bézier Smooth Semi-Supervised Support Vector Machine Regression

Abstract

Due to the excellent regression performance for semi-supervised learning, semi-supervised support vector machine (S3VR) is introduced for dealing with quantities of unlabeled data in the real world. However, the optimal objective function is not differentiable, which is required to suffer tedious calculation burden and decrease the regression performance. To address this problem, the smooth Bézier function has been investigated, and builds the novel method based on ε-insensitive loss function. This article presents one novel family of Bézier smooth semi-supervised support vector machine for ε-insensitive regression (ε-BS4VR). Firstly, the development of the novel series of ε-BS4VR regression is presented. Then, one fast algorithm for solving ε-BS4VR, the non-linear model, convergence and complexity analysis are submitted. To show how the ε-BS4VR is practically implemented, experiments are conducted on several benchmark and real-world datasets. The quantitative statistical analysis and experiments comparisons validate the feasibility and the effectiveness of the proposed method. In short, ε-BS4VR enhances the robustness of S3VR, and improves the comprehensive regression performance than other current semi-supervised models.