  Support vector machine (SVM) is a popular classifier known for accuracy,
flexibility, and robustness. However, its intensive computation has hindered
its application to large-scale datasets. In this paper, we propose a new
optimal leverage classifier based on linear SVM under a nonseparable setting.
Our classifier aims to select an informative subset of the training sample to
reduce data size, enabling efficient computation while maintaining high
accuracy. We take a novel view of SVM under the general subsampling framework
and rigorously investigate the statistical properties. We propose a two-step
subsampling procedure consisting of a pilot estimation of the optimal
subsampling probabilities and a subsampling step to construct the classifier.
We develop a new Bahadur representation of the SVM coefficients and derive
unconditional asymptotic distribution and optimal subsampling probabilities
without giving the full sample. Numerical results demonstrate that our
classifiers outperform the existing methods in terms of estimation,
computation, and prediction.
