Support vector machine with imprecise observation based on pinball loss

SVM is widely used in machine learning due to its simplicity, global optimization characteristics, and strong generalization ability. However, classical SVM assumes precise data, making it difficult to adapt to real-world data containing measurement errors and label noise. To address the problems of existing binary-class USVM models, such as poor adaptability to imbalanced data, this study proposes Pin-USVM that integrates uncertainty theory and pinball loss. Pinball loss provides asymmetric penalties for binary classification, proving especially suitable for scenarios where the cost of errors is imbalanced or categories exhibit imbalance. The model characterizes misclassification costs through τ-quantile distance and adjusts the tradeoff between outlier sensitivity and margin maximization via the τ parameter to improve the robustness of classification for uncertain data. Model hyperparameters are optimized using grid search with cross-validation, and experimental verification is conducted based on artificial and UCI datasets. The results show that Pin-USVM achieves higher classification accuracy for imbalanced binary classification data and outperforms the soft-margin USVM and FSVM even after adding noise. This study not only incorporates pinball loss into the USVM framework to enhance the model’s noise resistance and robustness, but also extends the application of USVM to imbalanced data classification, providing a viable solution for uncertain imbalanced binary classification problems.