Frank-Wolfe Algorithm for Exemplar Selection
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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 auto-regression. The set S, also known as the exemplars of the data set A, is constructed by solving a convex auto-regressive version of dictionary learning where the dictionary and measurements are given by the data matrix. We show that in order to generate |S| = k exemplars, our algorithm, Frank-Wolfe Sparse Representation (FWSR), only requires ≈ k iterations with a per-iteration cost that is quadratic in the size of A, an order of magnitude faster than state of the art methods. We test our algorithm against current methods on 4 different data sets and are able to outperform other exemplar finding methods in almost all scenarios. We also test our algorithm qualitatively by selecting exemplars from a corpus of Donald Trump and Hillary Clinton's twitter posts.
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