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Bilateral Random Projections

Abstract

Low-rank structure have been profoundly studied in data mining and machine learning. In this paper, we show a dense matrix XX's low-rank approximation can be rapidly built from its left and right random projections Y1=XA1Y_1=XA_1 and Y2=XTA2Y_2=X^TA_2, or bilateral random projection (BRP). We then show power scheme can further improve the precision. The deterministic, average and deviation bounds of the proposed method and its power scheme modification are proved theoretically. The effectiveness and the efficiency of BRP based low-rank approximation is empirically verified on both artificial and real datasets.Comment: 17 pages, 3 figures, technical repor

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