  We revisit vertex discriminant analysis (VDA) from the perspective of
proximal distance algorithms. By specifying sparsity sets as constraints that
directly control the number of active features, VDA is able to fit multiclass
classifiers with no more than $k$ active features. We combine our sparse VDA
approach with repeated cross validation to fit classifiers across the full
range of model sizes on a given dataset. Our numerical examples demonstrate
that grappling with sparsity directly is an attractive approach to model
building in high-dimensional settings. Applications to kernel-based VDA are
also considered.

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