Multi-view learning seeks to leverage the advantages of various views to complement each other and make full use of the latent information in the data. Nevertheless, effectively exploring and utilizing common and complementary information across diverse views remains challenging. In this paper, we propose two multi-view classifiers: multi-view support vector machine via L0/1 soft-margin loss (MvL0/1-SVM) and structural MvL0/1-SVM (MvSL0/1-SVM). The key difference between them is that MvSL0/1-SVM additionally fuses structural information, which simultaneously satisfies the consensus and complementarity principles. Despite the discrete nature inherent in the L0/1 soft-margin loss, we successfully establish the optimality theory for MvSL0/1-SVM. This includes demonstrating the existence of optimal solutions and elucidating their relationships with P-stationary points. Drawing inspiration from the P-stationary point optimality condition, we design and integrate a working set strategy into the proximal alternating direction method of multipliers. This integration significantly enhances the overall computational speed and diminishes the number of support vectors. Last but not least, numerical experiments show that our suggested models perform exceptionally well and have faster computational speed, affirming the rationality and effectiveness of our methods.

中文翻译：

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通过 [公式省略] 软边际损失和结构信息的多视图支持向量机分类器


多视图学习寻求利用各种视图的优势，相互补充，并充分利用数据中的潜在信息。然而，在不同观点中有效探索和利用共同和互补的信息仍然具有挑战性。在本文中，我们提出了两种多视图分类器：通过 L0/1 软边际损失 （MvL0/1-SVM） 和结构 MvL0/1-SVM （MvSL0/1-SVM） 的多视图支持向量机。它们之间的主要区别在于 MvSL0/1-SVM 还融合了结构信息，同时满足一致性和互补性原则。尽管 L0/1 软裕量损失具有固有的离散性，但我们成功地建立了 MvSL0/1-SVM 的最优性理论。这包括证明最优解的存在并阐明它们与 P 平稳点的关系。从 P 稳态点最优条件中汲取灵感，我们设计了一个工作集策略并将其集成到乘子的近端交替方向方法中。这种集成显著提高了整体计算速度并减少了支持向量的数量。最后但并非最不重要的一点是，数值实验表明，我们建议的模型性能非常好，计算速度更快，肯定了我们方法的合理性和有效性。