Consider a dataset of vector-valued observations that consists of a modest number of noisy inliers, which are explained well by a low-dimensional subspace, along with a large number of outliers, which have no linear structure. This work describes a convex optimization problem, called reaper, that can reliably t a low-dimensional model to this type of data. The paper provides an efficient algorithm for solving the reaper problem, and it documents numerical experiments which confirm that reaper can dependably nd linear structure in synthetic and natural data. In addition, when the inliers are contained in a low-dimensional subspace, there is a rigorous theory that describes when reaper can recover the subspace exactly.
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