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.

翻译：支持向量机（SVM）因成功实现了统计学习理论，作为分类器已获得广泛赞誉。然而，在多类和多标签场景中，现有SVM模型依赖向量形式化方法，在灵活性和易扩展性方面存在局限，难以通过添加额外项来处理特定挑战。为克服这些限制，本研究聚焦引入一种矩阵形式化的SVM，有效解决上述约束。通过在对偶问题中采用加速梯度下降法，我们显著提升了矩阵SVM问题的求解效率。在多标签和多类数据集上的实验评估表明，矩阵SVM在保持与二元关联SVM相似结果的同时，实现了更优的时间效能。此外，我们的矩阵形式化揭示了传统向量表示法中不易显现的关键见解与优势。我们强调，众多多标签模型可视为SVM的扩展，并通过定制化修改以满足特定需求。本文提出的矩阵形式化方法为开发更复杂的模型奠定了坚实基础，这些模型能够有效应对多标签学习中的独特挑战。