  Variable selection is essential in high-dimensional data analysis. Although
various variable selection methods have been developed, most rely on the linear
model assumption. This article proposes a nonparametric variable selection
method for the large-margin classifier defined by reproducing the kernel
Hilbert space (RKHS). we propose a gradient-based representation of the
large-margin classifier and then regularize the gradient functions by the
group-lasso penalty to obtain sparse gradients that naturally lead to the
variable selection. The groupwise-majorization-decent algorithm (GMD, Yang and
Zou, 2015) is proposed to efficiently solve the proposed problem with a large
number of parameters. We employ the strong sequential rule (Tibshirani et al.,
2012) to facilitate the tuning procedure. The selection consistency of the
proposed method is established by obtaining the risk bound of the estimated
classifier and its gradient. Finally, we demonstrate the promising performance
of the proposed method through simulations and real data illustration.
