The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Distributions of singular values for some random matrices
Open accessAbstract
The singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the distribution of singular values of low-rank matrices corrupted by additive noise. Past studies have been limited to uniform uncorrelated noise. Using diagrammatic and saddle point integration techniques, we extend these results to heterogeneous and correlated noise sources. We also provide perturbative estimates of error bars on the reconstructed low-rank matrix obtained by truncating a singular value decomposition.
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Cites
A planar diagram theory for strong interactions
Hooft, G. '. (1974) · Nuclear Physics B · doi:10.1016/0550-3213(74)90154-0 · Cited by 4,476
Extracting qualitative dynamics from experimental data
Broomhead, D. S., & King, G. P. (1986) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(86)90031-x · Cited by 2,278
Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains
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Visual stimuli induce waves of electrical activity in turtle cortex
Prechtl, J. C., Cohen, L. B., Pesaran, B., Mitra, P. P., & Kleinfeld, D. (1997) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.94.14.7621 · Cited by 328
Self-citationSingular-value decomposition and embedding dimension
Mees, A. I., Rapp, P. E., & Jennings, L. S. (1987) · Physical Review A · doi:10.1103/physreva.36.340 · Cited by 202
Mitra, P. P., Ogawa, S., Hu, X., & Uǧurbil, K. (1997) · Magnetic Resonance in Medicine · doi:10.1002/mrm.1910370407 · Cited by 185
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Cited by
Denoising of diffusion MRI using random matrix theory
Veraart, J., Novikov, D. S., Christiaens, D., Ades-aron, B., Sijbers, J., & Fieremans, E. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.08.016 · Cited by 1,905
Random matrix approach to cross correlations in financial data
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L. A. N., Guhr, T., & Stanley, H. E. (2002) · Physical Review E · doi:10.1103/physreve.65.066126 · Cited by 936
Replay of rule-learning related neural patterns in the prefrontal cortex during sleep
Peyrache, A., Khamassi, M., Benchenane, K., Wiener, S. I., & Battaglia, F. P. (2009) · Nature Neuroscience · doi:10.1038/nn.2337 · Cited by 767
Diffusion MRI noise mapping using random matrix theory
Veraart, J., Fieremans, E., & Novikov, D. S. (2016) · Magnetic Resonance in Medicine · doi:10.1002/mrm.26059 · Cited by 773
Physical approach to complex systems
Kwapień, J., & Drożdż, S. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.01.007 · Cited by 517
Metadata
- Authors
- Sengupta, A. M., & Mitra, P. P.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1999-09-01
- Volume
- 60
- Issue
- 3
- Pages
- 3389-3392
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W1989132237
- Cited by
- 358
- References
- 6
- FWCI
- 11.83
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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