A novel semi-supervised support vector machine with asymmetric squared loss

Laplacian support vector machine (LapSVM), which is based on the semi-supervised manifold regularization learning framework, performs better than the standard SVM, especially for the case where the supervised information is insufficient. However, the use of hinge loss leads to the sensitivity of LapSVM to noise around the decision boundary. To enhance the performance of LapSVM, we present a novel semi-supervised SVM with the asymmetric squared loss (asy-LapSVM) which deals with the expectile distance and is less sensitive to noise-corrupted data. We further present a simple and efficient functional iterative method to solve the proposed asy-LapSVM, in addition, we prove the convergence of the functional iterative method from two aspects of theory and experiment. Numerical experiments performed on a number of commonly used datasets with noise of different variances demonstrate the validity of the proposed asy-LapSVM and the feasibility of the presented functional iterative method.