Aiming at the problem that the traditional Twin Support Vector Machine (TSVM) is sensitive to noise and outliers, this paper proposes a twin support vector machine model based on generalized adaptive Huber loss function (GAHTSVM). Via dynamically adjusting the robust parameters $$s$$ , the model can effectively suppress the adverse effects of noisy data points on the decision function, and improve the sparsity of the model by introducing insensitive region design. For non-convex optimization problems, concave-convex process (CCCP) is adopted to avoid quadratic programming problems and significantly improve the efficiency of the algorithm. Experiments show that GAHTSVM performs well in the scenarios where Gaussian noise is added to real-world datasets and outliers are introduced to artificial datasets: it is significantly better than other algorithms in low noise environment; In the high noise environment, it still maintains a leading position, and most datasets are ranked in the top; It performs well on two artificial datasets and is significantly superior to other algorithms.In conclusion, the model effectively overcomes the noise and outlier interference by dynamically adjusting the outlier penalty, and provides an efficient solution to the pattern recognition problem in high noise environment.

Semi-supervised learning (SSL) based on manifold regularization in many fields has attracted widespread attention and research. However, SSL still has two main challenges: On the one hand, studies have shown that unlabeled data may cause performance degradation in semi-supervised classifiers, which means that unlabeled data introduces uncertainty and potential hazards. On the other hand, for samples distributed on different class boundaries, manifold regularization is not necessarily satisfactory, which will result in samples near the boundary that are likely to be misclassified. In response to the above problems, we propose a new SSL framework called safe semi-supervised learning (Sa-SSLJR for short). In Sa-SSLJR, a risk degree regularization term is constructed to estimate the uncertainty and potential risk of unlabeled data in the semi-supervised learning process. Secondly, based on manifold regularization and discriminant regularization, a joint regularization term is developed to solve the second challenge of SSL. Extensive experiments on multiple datasets show that our approach is competitive with state-of-the-art methods in terms of classification performance and feasibility.