Abstract: The Support Vector Machine (SVM) has been effective in various discrimination problems. Recently, there has been growing interest in extending the traditional vector-based SVM to accommodate structured matrix inputs. However, the nonsmooth hinge loss poses significant challenges for both theoretical and computational development. To address these issues, we propose a convex smoothing procedure for the hinge loss. Additionally, we introduce an elastic-net type penalty to handle high-dimensional matrix inputs. Our approach surpasses the standard SVM for discrimination involving high-dimensional matrix inputs. The proposed method provably achieves an optimal statistical convergence rate, and the smooth, convex loss function enables the development of a highly efficient optimization algorithm. This algorithm features a fast linear convergence rate and a simple implementation. Extensive simulations and an electroencephalography application demonstrate the method’s superiority in classification accuracy and computational efficiency.

Key words and phrases: Asymptotic theory, convolution-type smoothing, high-dimensional matrix regression, linear support vector machines.