Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on vector-based formulations in existing SVM-based models poses limitations regarding flexibility and ease of incorporating additional terms to handle specific challenges. To overcome these limitations, our research paper focuses on introducing a matrix formulation for SVM that effectively addresses these constraints. By employing the Accelerated Gradient Descent method in the dual, we notably enhance the efficiency of solving the Matrix-SVM problem. Experimental evaluations on multilabel and multiclass datasets demonstrate that Matrix SVM achieves superior time efficacy while delivering similar results to Binary Relevance SVM. Moreover, our matrix formulation unveils crucial insights and advantages that may not be readily apparent in traditional vector-based notations. We emphasize that numerous multilabel models can be viewed as extensions of SVM, with customised modifications to meet specific requirements. The matrix formulation presented in this paper establishes a solid foundation for developing more sophisticated models capable of effectively addressing the distinctive challenges encountered in multilabel learning.

支持向量机(SVM)在统计学习理论的成功应用方面获得了显著的赞誉。然而，在多类和多标签设置环境中，现有基于向量表示的SVM模型的依赖性对于灵活性和易于整合附加项以处理特定挑战方面存在局限性。为了克服这些限制，我们的研究重点介绍了一个有效解决这些约束的SVM矩阵形式。通过在对偶问题中应用加速梯度下降方法，我们显著提高了解决矩阵-SVM问题的效率。对多标签和多类数据集的实验评估表明，矩阵SVM实现了更高的时间效率，并且与二元相关SVM的结果相似。此外，我们的矩阵形式揭示了在传统基于向量符号中可能不容易察觉的重要见解和优势。我们强调，许多多标签模型可以被视为SVM的扩展，通过定制修改以满足特定要求。本文提出的矩阵形式为开发更复杂的模型奠定了坚实的基础，能够有效应对多标签学习中遇到的独特挑战。

通过矩阵公式增强支持向量机中的模式分类