The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Improved Approximation Algorithms for Large Matrices via Random Projections
Abstract
Several results appeared that show significant reduction in time for matrix multiplication, singular value decomposition as well as linear (lscr2) regression, all based on data dependent random sampling. Our key idea is that low dimensional embeddings can be used to eliminate data dependence and provide more versatile, linear time pass efficient matrix computation. Our main contribution is summarized as follows. 1) Independent of the results of Har-Peled and of Deshpande and Vempala, one of the first - and to the best of our knowledge the most efficient - relative error (1 + epsi) parA $AkparFapproximation algorithms for the singular value decomposition of an m times n matrix A with M non-zero entries that requires 2 passes over the data and runs in time O((M(k/epsi+k log k) + (n+m)(k/epsi+k log k)2)log (1/sigma)). 2) The first o(nd2) time (1 + epsi) relative error approximation algorithm for n times d linear (lscr2) regression. 3) A matrix multiplication and norm approximation algorithm that easily applies to implicitly given matrices and can be used as a black box probability boosting tool
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Approximate nearest neighbors: towards removing the curse of dimensionality
Indyk, P., & Motwani, R. (1998) · Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98 · doi:10.1145/276698.276876 · Cited by 4,188
Matrix multiplication via arithmetic progressions
Coppersmith, D., & Winograd, S. (1990) · Journal of Symbolic Computation · doi:10.1016/s0747-7171(08)80013-2 · Cited by 2,248
Cited by
A Randomized Algorithm for Principal Component Analysis
Rokhlin, V., Szlam, A., & Tygert, M. (2010) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/080736417 · Cited by 422
Numerical linear algebra in the streaming model
Clarkson, K. L., & Woodruff, D. P. (2009) · Proceedings of the forty-first annual ACM symposium on Theory of computing · doi:10.1145/1536414.1536445 · Cited by 301
New and Improved Johnson–Lindenstrauss Embeddings via the Restricted Isometry Property
Krahmer, F., & Ward, R. (2011) · SIAM Journal on Mathematical Analysis · doi:10.1137/100810447 · Cited by 290
A fast randomized algorithm for the approximation of matrices
Woolfe, F., Liberty, E., Rokhlin, V., & Tygert, M. (2008) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2007.12.002 · Cited by 280
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
Brunton, S. L., Nathan Kutz, J., Manohar, K., Aravkin, A. Y., Morgansen, K., Klemisch, J., Goebel, N., Buttrick, J., Poskin, J., Blom-Schieber, A. W., et al. (2021) · AIAA Journal · doi:10.2514/1.j060131 · Cited by 270
Metadata
- Authors
- Sarlos, T.
- Venue
- 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
- Publisher
- IEEE
- Published
- 2006-10
- Pages
- 143-152
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2045390367
- Cited by
- 646
- References
- 3
- FWCI
- 10.66
- Type
- conference paper
- Language
- en
- Open access
- closed
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