385 research outputs found

    Bilateral Random Projections

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    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

    Hamming Compressed Sensing

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    Compressed sensing (CS) and 1-bit CS cannot directly recover quantized signals and require time consuming recovery. In this paper, we introduce \textit{Hamming compressed sensing} (HCS) that directly recovers a k-bit quantized signal of dimensional nn from its 1-bit measurements via invoking nn times of Kullback-Leibler divergence based nearest neighbor search. Compared with CS and 1-bit CS, HCS allows the signal to be dense, takes considerably less (linear) recovery time and requires substantially less measurements (O(log⁑n)\mathcal O(\log n)). Moreover, HCS recovery can accelerate the subsequent 1-bit CS dequantizer. We study a quantized recovery error bound of HCS for general signals and "HCS+dequantizer" recovery error bound for sparse signals. Extensive numerical simulations verify the appealing accuracy, robustness, efficiency and consistency of HCS.Comment: 33 pages, 8 figure
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