Fetching the paper…
Reading the bibliography…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset.
Hellmuth Kneser, Sur un théoreme fondamental de la théorie des jeux , Comptes Rendus de l’Academie des Sciences 234
1952
Earlier work this paper cites.
Theodore Wilbur Anderson, Asymptotic theory for principal component analysis , Annals of Mathematical Statistics (1963), 122–148
1963
Earlier work this paper cites.
Charles Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables , Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 1972
1972
Earlier work this paper cites.
David J. Thouless, Philip W. Anderson, and Robert G. Palmer, Solution of’solvable model of a spin glass’ , Philosophical Magazine 35
1977
Earlier work this paper cites.
Marc Mézard, Giorgio Parisi, and Miguel A. Virasoro, Spin glass theory and beyond , World Scientific, 1987
1987
Earlier work this paper cites.
David L. Donoho and Iain M. Johnstone, Neo-classical minimax problems, thresholding, and adaptation , Bernoulli (1994), 39–62
1994
Earlier work this paper cites.
Pentti Paatero and Unto Tapper, Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values , Environmetrics 5
1994
Earlier work this paper cites.
Pentti Paatero, Least squares formulation of robust non-negative factor analysis , Chemometrics and intelligent laboratory systems 37
1997
Earlier work this paper cites.
Michael S Lewicki, A review of methods for spike sorting: the detection and classification of neural action potentials , Network: Computation in Neural Systems 9
1998
Earlier work this paper cites.
Christopher M Bishop, Bayesian pca , Advances in neural information processing systems (1999), 382–388
1999
Earlier work this paper cites.
Daniel D Lee and H Sebastian Seung, Learning the parts of objects by non-negative matrix factorization , Nature 401
1999
Earlier work this paper cites.
Richard A Vitale, Some comparisons for gaussian processes , Proceedings of the American Mathematical Society (2000), 3043–3046
2000
Earlier work this paper cites.
Glen D Brown, Satoshi Yamada, and Terrence J Sejnowski, Independent component analysis at the neural cocktail party , Trends in neurosciences 24
2001
Earlier work this paper cites.
Etienne de Klerk and Dmitrii V Pasechnik, Approximation of the stability number of a graph via copositive programming , SIAM Journal on Optimization 12
2002
Earlier work this paper cites.
Laura Lazzeroni and Art Owen, Plaid models for gene expression data , Statistica sinica 12
2002
Earlier work this paper cites.
Amos Tanay, Roded Sharan, and Ron Shamir, Discovering statistically significant biclusters in gene expression data , Bioinformatics 18
2002
Earlier work this paper cites.
David L Donoho and Victoria Stodden, When does non-negative matrix factorization give a correct decomposition into parts? , NIPS, vol. 16, 2003
2003
Earlier work this paper cites.
Yuval Kluger, Ronen Basri, Joseph T Chang, and Mark Gerstein, Spectral biclustering of microarray data: coclustering genes and conditions , Genome research 13
2003
Earlier work this paper cites.
Iain M Johnstone and Arthur Yu Lu, Sparse principal components analysis , Unpublished manuscript (2004)
2004
Earlier work this paper cites.
Sara C Madeira and Arlindo L Oliveira, Biclustering algorithms for biological data analysis: a survey , Computational Biology and Bioinformatics, IEEE/ACM Transactions on 1
2004
Earlier work this paper cites.
R Quian Quiroga, Zoltan Nadasdy, and Yoram Ben-Shaul, Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering , Neural computation 16
2004
Earlier work this paper cites.
2004
Earlier work this paper cites.
Jinho Baik, Gérard Ben Arous, and Sandrine Péché, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices , Annals of Probability (2005), 1643–1697
2005
Cited alongside, same era.
Sourav Chatterjee, An error bound in the Sudakov-Fernique inequality , http://arxiv.org/pdf/math/0510424v1.pdf, 2005
2005
Cited alongside, same era.
Jinho Baik and Jack W Silverstein, Eigenvalues of large sample covariance matrices of spiked population models , Journal of Multivariate Analysis 97
2006
Cited alongside, same era.
Hui Zou, Trevor Hastie, and Robert Tibshirani, Sparse principal component analysis , Journal of computational and graphical statistics 15
2006
Cited alongside, same era.
Debashis Paul, Asymptotics of sample eigenstructure for a large dimensional spiked covariance model , Statistica Sinica 17
2007
Mireille Capitaine, Catherine Donati-Martin, Delphine Féral, Maxime Février, et al., Free convolution with a semicircular distribution and eigenvalues of spiked deformations of Wigner matrices , Electron. J. Probab 16
2011
Later among the works it cites.
Iain M. Johnstone, Gaussian estimation: Sequence and wavelet models , 2011, Draft version, December 27, 2011, available at http://statweb.stanford.edu/ imj/GE12-27-11.pdf
2011
Later among the works it cites.
Sundeep Rangan, Generalized Approximate Message Passing for Estimation with Random Linear Mixing , IEEE Intl. Symp. on Inform. Theory (St. Perersbourg), August 2011
2011
Later among the works it cites.
Philip Schniter and Volkan Cevher, Approximate message passing for bilinear models , Proc. Workshop Signal Process. Adaptive Sparse Struct. Repr.(SPARS), 2011, p. 68
2011
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Alexey Pavlov, Valeri A Makarov, Ioulia Makarova, and Fivos Panetsos, Sorting of neural spikes: when wavelet based methods outperform principal component analysis , Natural Computing 6
2007
Cited alongside, same era.
Thomas J. Richardson and Rüdiger Urbanke, Modern Coding Theory , Cambridge University Press, Cambridge, 2008
2008
Cited alongside, same era.
Greg W. Anderson, Alice Guionnet, and Ofer Zeitouni, An introduction to random matrices , Cambridge University Press, 2009
2009
Cited alongside, same era.
Samuel Burer, Kurt M. Anstreicher, and Mirjam Dur, The difference between 5 × \times 5 doubly nonnegative and completely positive matrices , Linear Algebra and its Applications 431(9)
2009
Cited alongside, same era.
Mireille Capitaine, Catherine Donati-Martin, and Delphine Féral, The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations , The Annals of Probability 37
2009
Cited alongside, same era.
D. L. Donoho, A. Maleki, and A. Montanari, Message Passing Algorithms for Compressed Sensing , Proceedings of the National Academy of Sciences 106
2009
Cited alongside, same era.
Delphine Féral and Sandrine Péché, The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case , Journal of Mathematical Physics 50
2009
Cited alongside, same era.
Jeremy Vila and Philip Schniter, Expectation-maximization bernoulli-gaussian approximate message passing , Proc. Asilomar Conf. on Signals, Systems, and Computers (Pacific Grove, CA), 2011
2011
Later among the works it cites.
Sanjeev Arora, Rong Ge, Ravindran Kannan, and Ankur Moitra, Computing a nonnegative matrix factorization–provably , Proceedings of the 44th symposium on Theory of Computing, ACM, 2012, pp. 145–162
2012
Later among the works it cites.
Florent Benaych-Georges, Alice Guionnet, and Mylène Maïda, Large deviations of the extreme eigenvalues of random deformations of matrices , Probability Theory and Related Fields 154
2012
Later among the works it cites.
2012
Later among the works it cites.
Mireille Capitaine, Catherine Donati-Martin, and Delphine Féral, Central limit theorems for eigenvalues of deformations of Wigner matrices , Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 48, Institut Henri Poincaré, 2012, pp. 107–133
2012
Later among the works it cites.
Aandrea Montanari, Graphical Models Concepts in Compressed Sensing , Compressed Sensing: Theory and Applications (Y.C. Eldar and G. Kutyniok, eds.), Cambridge University Press, 2012
2012
Later among the works it cites.
2013
Later among the works it cites.
Adel Javanmard and Andrea Montanari, State evolution for general approximate message passing algorithms, with applications to spatial coupling , Information and Inference 2
2013
Later among the works it cites.
2013
Later among the works it cites.
Antti Knowles and Jun Yin, The isotropic semicircle law and deformation of Wigner matrices , Communications on Pure and Applied Mathematics (2013)
2013
Later among the works it cites.
Zongming Ma, Sparse principal component analysis and iterative thresholding , The Annals of Statistics 41
2013
Later among the works it cites.
Alessandro Pizzo, David Renfrew, and Alexander Soshnikov, On finite rank deformations of Wigner matrices , Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 49, Institut Henri Poincaré, 2013, pp. 64–94
2013
Later among the works it cites.
2013
Later among the works it cites.
Xing Sun and Andrew B Nobel, On the maximal size of large-average and anova-fit submatrices in a gaussian random matrix , Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability 19
2013
Later among the works it cites.
Jeremy Vila, Philip Schniter, and Joseph Meola, Hyperspectral image unmixing via bilinear generalized approximate message passing , SPIE Defense, Security, and Sensing, International Society for Optics and Photonics, 2013, pp. 87430Y–87430Y
2013
Later among the works it cites.
Xiao-Tong Yuan and Tong Zhang, Truncated power method for sparse eigenvalue problems , The Journal of Machine Learning Research 14
2013
Later among the works it cites.