Tropp, Joel A. and Yurtsever, Alp and Udell, Madeleine and Cevher, Volkan (2017) Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data. In: 31st Conference on Neural Information Processing Systems (NIPS 2017), 4-9 December 2017, Long Beach, CA. https://resolver.caltech.edu/CaltechAUTHORS:20180829-073029156
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Abstract
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nyström approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exploits the spectral decay of the input matrix. Computer experiments show that the proposed method dominates alternative techniques for fixed-rank psd matrix approximation across a wide range of examples.
Item Type: | Conference or Workshop Item (Paper) | ||||||||||||
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Additional Information: | The authors wish to thank Mark Tygert and Alex Gittens for helpful feedback on preliminary versions of this work. JAT gratefully acknowledges partial support from ONR Award N00014-17-1-2146 and the Gordon & Betty Moore Foundation. VC and AY were supported in part by the European Commission under Grant ERC Future Proof, SNF 200021-146750, and SNF CRSII2-147633. MU was supported in part by DARPA Award FA8750-17-2-0101. | ||||||||||||
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Record Number: | CaltechAUTHORS:20180829-073029156 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180829-073029156 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 89267 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 29 Aug 2018 16:45 | ||||||||||||
Last Modified: | 03 Oct 2019 20:14 |
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