The DOI matches its Crossref record; 29 of the 29 references it cites were found in a registry or an index.
A Randomized Algorithm for Principal Component Analysis
Abstract
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a few digits (measured in the spectral norm, relative to the spectral norm of the matrix being approximated). In such circumstances, efficient algorithms have not come with guarantees of good accuracy, unless one or both dimensions of the matrix being approximated are small. We describe an efficient algorithm for the low-rank approximation of matrices that produces accuracy that is very close to the best possible accuracy, for matrices of arbitrary sizes. We illustrate our theoretical results via several numerical examples.
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Randomized algorithms for the low-rank approximation of matrices
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., & Tygert, M. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709640104 · Cited by 559
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Scikit-learn: Machine Learning in Python
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Müller, A., Nothman, J., Louppe, G., et al. (2012) · arXiv · doi:10.48550/arxiv.1201.0490 · Cited by 71,016
Machine Learning for Fluid Mechanics
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Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis
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Machine Learning Methods for Small Data Challenges in Molecular Science
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Fast nonnegative deconvolution for spike train inference from population calcium imaging
Vogelstein, J. T., Packer, A. M., Machado, T. A., Sippy, T., Babadi, B., Yuste, R., & Paninski, L. (2010) · Journal of Neurophysiology · doi:10.1152/jn.01073.2009 · Cited by 449
Metadata
- Authors
- Rokhlin, V., Szlam, A., & Tygert, M.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2010-01
- Volume
- 31
- Issue
- 3
- Pages
- 1100-1124
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2040387238
- Cited by
- 422
- References
- 29
- FWCI
- 17.38
- Type
- journal article
- Language
- en
- Open access
- closed
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