Laplacian twin parametric-margin support vector machine for semi-supervised classification

As an extension of twin support vector machine (TSVM), twin parametric-margin support vector machine (TPMSVM) makes the learning speed faster than that of the parametric-margin ν-support vector machine (par-ν-SVM), and it is suitable for many cases, especially when the data has heteroscedastic error structure. This algorithm needs all the labels of training samples, which belongs to a supervised method. However, it is sometimes difficult to achieve each label of the data. To effectively handle this case, we propose a Laplacian twin parametric-margin support vector machine (LTPMSVM) for the semi-supervised classification, which exploits the geometric information of the marginal distribution embedded in unlabeled data to construct a more reasonable classifier. Additionally, the LTPMSVM has helpful properties to shed light on theoretical interpretation of parameters which control the bounds on proportions of support vectors and boundary errors. Experimental results on artificial datasets testify the properties of its parameters. Furthermore, results on the ABCDETC and twelve benchmark datasets indicate that our proposed LTPMSVM yields a good generalization performance with the comparable computing time to Laplacian twin support vector machine (LTSVM).