We introduce a novel twin support vector machine with the generalized pinball loss function (GPin-TSVM) for solving data classification problems that are less sensitive to noise and preserve the sparsity of the solution. In addition, we use a symmetric kernel trick to enlarge GPin-TSVM to nonlinear classification problems. The developed approach is tested on numerous UCI benchmark datasets, as well as synthetic datasets in the experiments. The comparisons demonstrate that our proposed algorithm outperforms existing classifiers in terms of accuracy. Furthermore, this employed approach in handwritten digit recognition applications is examined, and the automatic feature extractor employs a convolution neural network.

Semi-supervised learning utilizes labeled data and the geometric information in the unlabeled data to construct a model whereas supervised learning makes use of the only label data. So, semi-supervised learning establishes a more reasonable classifier. In recent years, the Laplacian support vector machine (Lap-SVM) has received a lot of interest in the framework of semi-supervised classification. To develop the performance of Lap-SVM, Laplacian twin support vector machine (Lap-TSVM) has shown exceptional performance as an addition to improve the computational complexity. However, dealing with noise sensitivity and instability for resampling due to its hinge loss function is still a challenge. In this paper, we provide a novel Laplacian twin support vector machine by combining pinball loss function, termed as Lap-PTSVM, to effectively handle the aforementioned problems. As a result, it improves a better generalization ability of the classifier. Several experiments have been performed on artificial and UCI datasets. The results show that the proposed model has noise insensitivity comparable to the Lap-TSVM and has a great generalization performance. Furthermore, non-parametric statistical test are also conducted to justify the competitive performance of Lap-PTSVM.

In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.