Noisy Power Method with Grassmann Average

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The power method is a simple and efficient algorithm for finding the top k singular vectors of any input matrix. In practice, noise matrices could be added to the input matrix at each iteration of the power method, and the convergence behavior of the algorithm is hard to guarantee. The convergence behavior of the noisy power method is understood only for the cases when the noise level (the spectral norm of noise matrices) is bellow a threshold and the noisy power method cannot extract the exact top k singular vectors because of the noise matrices. We propose a Grassmann average function which can make the noisy power method converge to the exact top k singular vectors and an efficient algorithm that can approximate the Grassmann average with a much less computational cost.
Publisher
IEEE
Issue Date
2018-01
Language
English
Citation

2018 IEEE International Conference on Big Data and Smart Computing (BigComp), pp.709 - 712

DOI
10.1109/bigcomp.2018.00132
URI
http://hdl.handle.net/10203/272921
Appears in Collection
RIMS Conference Papers
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