Reconstruction of a low-rank matrix in the presence of Gaussian noise
Author
Abstract
Suggested Citation
DOI: 10.1016/j.jmva.2013.03.005
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- L. Györfi & I. Vajda & E. Meulen, 1996. "Minimum kolmogorov distance estimates of parameters and parametrized distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 237-255, December.
- Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
- Yata, Kazuyoshi & Aoshima, Makoto, 2012. "Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 193-215.
- Dozier, R. Brent & Silverstein, Jack W., 2007. "On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 678-694, April.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Hyung-Il Kim & Seok Bong Yoo, 2020. "Trends in Super-High-Definition Imaging Techniques Based on Deep Neural Networks," Mathematics, MDPI, vol. 8(11), pages 1-19, October.
- Junhui Cai & Dan Yang & Wu Zhu & Haipeng Shen & Linda Zhao, 2021. "Network regression and supervised centrality estimation," Papers 2111.12921, arXiv.org.
- Li, Gen & Yang, Dan & Nobel, Andrew B. & Shen, Haipeng, 2016. "Supervised singular value decomposition and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 7-17.
- Leeb, William, 2022. "Optimal singular value shrinkage for operator norm loss: Extending to non-square matrices," Statistics & Probability Letters, Elsevier, vol. 186(C).
- Gen Li & Sungkyu Jung, 2017. "Incorporating covariates into integrated factor analysis of multi‐view data," Biometrics, The International Biometric Society, vol. 73(4), pages 1433-1442, December.
- Bigot, Jérémie & Deledalle, Charles, 2022. "Low-rank matrix denoising for count data using unbiased Kullback-Leibler risk estimation," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
- Gong, Tingnan & Zhang, Weiping & Chen, Yu, 2023. "Uncovering block structures in large rectangular matrices," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
- Yata, Kazuyoshi & Aoshima, Makoto, 2013. "Correlation tests for high-dimensional data using extended cross-data-matrix methodology," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 313-331.
- Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
- Bai, Zhidong & Wang, Chen, 2015. "A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 333-340.
- Jung, Sungkyu & Sen, Arusharka & Marron, J.S., 2012. "Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 190-203.
- Forzani, Liliana & Gieco, Antonella & Tolmasky, Carlos, 2017. "Likelihood ratio test for partial sphericity in high and ultra-high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 18-38.
- Wang, Shao-Hsuan & Huang, Su-Yun, 2022. "Perturbation theory for cross data matrix-based PCA," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
- Michael Bridges & Elizabeth A Heron & Colm O'Dushlaine & Ricardo Segurado & The International Schizophrenia Consortium (ISC) & Derek Morris & Aiden Corvin & Michael Gill & Carlos Pinto, 2011. "Genetic Classification of Populations Using Supervised Learning," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-12, May.
- Hachem, Walid & Loubaton, Philippe & Mestre, Xavier & Najim, Jamal & Vallet, Pascal, 2013. "A subspace estimator for fixed rank perturbations of large random matrices," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 427-447.
- Nick Patterson & Alkes L Price & David Reich, 2006. "Population Structure and Eigenanalysis," PLOS Genetics, Public Library of Science, vol. 2(12), pages 1-20, December.
- Brendan P. W. Ames & Mingyi Hong, 2016. "Alternating direction method of multipliers for penalized zero-variance discriminant analysis," Computational Optimization and Applications, Springer, vol. 64(3), pages 725-754, July.
- Ding, Xiucai & Ji, Hong Chang, 2023. "Spiked multiplicative random matrices and principal components," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 25-60.
- Shu Wang & Jia-Ren Lin & Eduardo D Sontag & Peter K Sorger, 2019. "Inferring reaction network structure from single-cell, multiplex data, using toric systems theory," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-25, December.
- Feldman, Michael J., 2023. "Spiked singular values and vectors under extreme aspect ratios," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
- Bo Zhang & Jiti Gao & Guangming Pan & Yanrong Yang, 2019. "Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices," Monash Econometrics and Business Statistics Working Papers 31/19, Monash University, Department of Econometrics and Business Statistics.
- Li, Weiming & Zhu, Junpeng, 2023. "CLT for spiked eigenvalues of a sample covariance matrix from high-dimensional Gaussian mean mixtures," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
- Collins, Benoît & Matsumoto, Sho & Saad, Nadia, 2014. "Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 1-13.
- Passemier, Damien & Yao, Jianfeng, 2014. "Estimation of the number of spikes, possibly equal, in the high-dimensional case," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 173-183.
- Paul, Debashis & Silverstein, Jack W., 2009. "No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 37-57, January.
- Wang, Qinwen & Silverstein, Jack W. & Yao, Jian-feng, 2014. "A note on the CLT of the LSS for sample covariance matrix from a spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 194-207.
More about this item
Keywords
Matrix reconstruction; Random matrix theory; Eigenvalue distribution; Eigenvector distribution; HDLSS; Principal component analysis;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:67-76. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.