The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Fast computation of low-rank matrix approximations
Abstract
Given a matrix A , it is often desirable to find a good approximation to A that has low rank. We introduce a simple technique for accelerating the computation of such approximations when A has strong spectral features, that is, when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to A . Our technique amounts to independently sampling and/or quantizing the entries of A , thus speeding up computation by reducing the number of nonzero entries and/or the length of their representation. Our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix N to A , whose entries are independent random variables with zero-mean and bounded variance. Since, with high probability, N has very weak spectral features, we can prove that the effect of sampling and quantization nearly vanishes when a low-rank approximation to A + N is computed. We give high probability bounds on the quality of our approximation both in the Frobenius and the 2-norm.
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Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
Drineas, P., Kannan, R., & Mahoney, M. W. (2006) · SIAM Journal on Computing · doi:10.1137/s0097539704442696 · Cited by 552
A Randomized Algorithm for Principal Component Analysis
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Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
Chi, Y., Lu, Y. M., & Chen, Y. (2019) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2019.2937282 · Cited by 360
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Metadata
- Authors
- Achlioptas, D., & Mcsherry, F.
- Venue
- Journal of the ACM
- Published
- 2007-04
- Volume
- 54
- Issue
- 2
- Pages
- 9
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W1970950689
- Cited by
- 292
- References
- 16
- FWCI
- 16.14
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
