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• W2990379149 abstract "This paper studies spectral approximation for a positive semidefinite matrix in the online setting. It is known in [Cohen et al. APPROX 2016] that we can construct a spectral approximation of a given $n times d$ matrix in the online setting if an additive error is allowed. In this paper, we propose an online algorithm that avoids an additive error with the same time and space complexities as the algorithm of Cohen et al., and provides a better upper bound on the approximation size when a given matrix has small rank. In addition, we consider the online random order setting where a row of a given matrix arrives uniformly at random. In this setting, we propose time and space efficient algorithms to find a spectral approximation. Moreover, we reveal that a lower bound on the approximation size in the online random order setting is $Omega (d epsilon^{-2} log n)$, which is larger than the one in the offline setting by an $mathrm{O}left( log n right)$ factor." @default.
• W2990379149 created "2019-12-05" @default.
• W2990379149 creator A5014143187 @default.
• W2990379149 creator A5047111221 @default.
• W2990379149 date "2019-11-20" @default.
• W2990379149 modified "2023-10-01" @default.
• W2990379149 title "Online Spectral Approximation in Random Order Streams" @default.
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• W2990379149 hasPublicationYear "2019" @default.
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