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A new truncated non-convex loss based support vector machine for robust binary classification
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AI
DOI：10.1007/s10489-025-06799-2.png)
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Abstract
En 中文
Recently, support vector machines (SVMs) based on bounded loss functions have attracted significant attention due to their robustness. In this paper, we propose a novel non-convex, monotonic, and bounded loss function called the $$\epsilon$$ -insensitive truncated non-convex ( $$\epsilon$$ -TNC) loss, and construct our $$\epsilon$$ -TNCSVM model by replacing the hinge loss with the proposed $$\epsilon$$ -TNC loss in the standard SVM. The non-convexity and boundedness enhance the robustness of the model, and we innovatively use the influence function of the estimator to demonstrate this theoretically. Monotonicity ensures that the $$\epsilon$$ -TNCSVM retains the sparsity of the traditional SVM model. Besides, we demonstrate that $$\epsilon$$ -TNCSVM satisfies Fisher consistency and obtains the corresponding generalization error bound based on Rademacher complexity, guaranteeing its good generalization capability. However, the non-convexity of the proposed $$\epsilon$$ -TNC loss makes it difficult to optimize. Hence, a non-convex optimization method, the concave-convex procedure (CCCP) technique, is implemented to solve the proposed model. We conduct various experiments to verify the effectiveness of our proposed $$\epsilon$$ -TNCSVM model.
Keywords:
Binary classification
\(\epsilon\) -TNC loss
Robustness
CCCP technique
Influence function