  In this paper, we consider the problem of selecting representatives from a
data set for arbitrary supervised/unsupervised learning tasks. We identify a
subset $S$ of a data set $A$ such that 1) the size of $S$ is much smaller than
$A$ and 2) $S$ efficiently describes the entire data set, in a way formalized
via convex optimization. In order to generate $|S| = k$ exemplars, our
kernelizable algorithm, Frank-Wolfe Sparse Representation (FWSR), only needs to
execute $\approx k$ iterations with a per-iteration cost that is quadratic in
the size of $A$. This is in contrast to other state of the art methods which
need to execute until convergence with each iteration costing an extra factor
of $d$ (dimension of the data). Moreover, we also provide a proof of linear
convergence for our method. We support our results with empirical experiments;
we test our algorithm against current methods in three different experimental
setups on four different data sets. FWSR outperforms other exemplar finding
methods both in speed and accuracy in almost all scenarios.
