Convoluted Support Matrix Machine in High Dimensions

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.