Year: 2024
Type: article
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.
Source: Statistica Sinica
Authors: Bingzhen Chen, Canyi Chen
Institutions: University of Michigan, Hangzhou Dianzi University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Hangzhou Dianzi University
OpenAlex ID: W4402588566