Conventional sampling techniques fall short of drawing descriptive sketchesof the data when the data is grossly corrupted as such corruptions break thelow rank structure required for them to perform satisfactorily. In this paper,we present new sampling algorithms which can locate the informative columns inpresence of severe data corruptions. In addition, we develop new scalablerandomized designs of the proposed algorithms. The proposed approach issimultaneously robust to sparse corruption and outliers and substantiallyoutperforms the state-of-the-art robust sampling algorithms as demonstrated byexperiments conducted using both real and synthetic data.
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