Distributed Estimation of Support Vector Machines for Matrix Data

Discrimination problems are of significant interest in the machine learning literature. There has been growing interest in extending traditional vector-based machine learning techniques to their matrix forms. In this article, we investigate the statistical properties of the nuclear-norm-based regularized linear support vector machines (SVMs), in particular establishing the convergence rate of the estimator in the high-dimensional setting. Furthermore, within the distributed estimation paradigm, we propose a communication-efficient estimator that can achieve the same convergence rate. We illustrate the performances of the estimators via some simulation examples and an empirical data analysis.