Enhancing Pattern Classification in Support Vector Machines through
  Matrix Formulation
Sambhav Jain Reshma Rastogi
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.