Fetching the paper…
Reading the bibliography…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications.
1902
Earlier work this paper cites.
G. Young, “Maximum likelihood estimation and factor analysis,” Psychometrika , vol. 6, no. 1, pp. 49–53, Feb. 1941
1941
Earlier work this paper cites.
M. Marden, Geometry of Polynomials . American Mathematical Society, Dec. 1949
1949
Earlier work this paper cites.
D. Lawley, “A modified method of estimation in factor analysis and some large sample results,” in Uppsala symposium on psychological factor analysis , vol. 17, no. 19. Taylor & Francis, 1953, pp. 35–42
1953
Earlier work this paper cites.
T. W. Anderson and H. Rubin, “Statistical inference in factor analysis,” in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume 5: Contributions to Econometrics, Industrial Research, and Psychometry . University of California Press, 1956, pp. 111–150
1956
Earlier work this paper cites.
M. J. D. Powell, “On search directions for minimization algorithms,” Mathematical Programming , vol. 4, no. 1, pp. 193–201, 1973
1973
Earlier work this paper cites.
R. N. Cochran and F. H. Horne, “Statistically weighted principal component analysis of rapid scanning wavelength kinetics experiments,” Analytical Chemistry , vol. 49, no. 6, pp. 846–853, May 1977
1977
Earlier work this paper cites.
D. B. Rubin and D. T. Thayer, “EM algorithms for ML factor analysis,” Psychometrika , vol. 47, no. 1, pp. 69–76, Mar. 1982
1982
Earlier work this paper cites.
J. A. Fessler and A. O. Hero, “Space-alternating generalized expectation-maximization algorithm,” IEEE Transactions on Signal Processing , vol. 42, no. 10, pp. 2664–2677, 1994
1994
Earlier work this paper cites.
A. R. De Pierro, “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography,” IEEE Trans. Med. Imag. , vol. 14, no. 1, pp. 132–7, Mar. 1995
1995
Earlier work this paper cites.
S. T. Roweis, “EM Algorithms for PCA and SPCA,” in Advances in Neural Information Processing Systems . MIT Press, 1998, pp. 626–632
1998
Earlier work this paper cites.
H. Hong, “Bounds for absolute positiveness of multivariate polynomials,” Journal of Symbolic Computation , vol. 25, no. 5, pp. 571–585, May 1998
1998
Earlier work this paper cites.
M. E. Tipping and C. M. Bishop, “Probabilistic Principal Component Analysis,” Journal of the Royal Statistical Society: Series B (Statistical Methodology) , vol. 61, no. 3, pp. 611–622, Aug. 1999
1999
Earlier work this paper cites.
M. Tipping, “Sparse kernel principal component analysis,” in Neural Info. Proc. Sys. , vol. 13, 2001. [Online]. Available: https://papers.nips.cc/paper/2000/hash/bf201d5407a6509fa536afc4b380577e-Abstract.html
2000
Earlier work this paper cites.
I. T. Jolliffe, Principal Component Analysis . Springer-Verlag, 2002
2002
Earlier work this paper cites.
A. I. Schein, L. K. Saul, and L. H. Ungar, “A generalized linear model for principal component analysis of binary data,” in International Workshop on Artificial Intelligence and Statistics . PMLR, 2003, pp. 240–247
2003
Earlier work this paper cites.
Y. Chikuse, Statistics on Special Manifolds . Springer New York, 2003
2003
Earlier work this paper cites.
O. Tamuz, T. Mazeh, and S. Zucker, “Correcting systematic effects in a large set of photometric light curves,” Monthly Notices of the Royal Astronomical Society , vol. 356, no. 4, pp. 1466–1470, Feb. 2005
2005
Earlier work this paper cites.
N. Lawrence, “Probabilistic non-linear principal component analysis with Gaussian process latent variable models,” J. Mach. Learning Res. , vol. 6, no. 60, pp. 1783–816, 2005. [Online]. Available: http://jmlr.org/papers/v6/lawrence05a.html
2005
Earlier work this paper cites.
2006
Earlier work this paper cites.
2007
Cited alongside, same era.
R. E. Moore, R. B. Kearfott, and M. J. Cloud, Introduction to Interval Analysis . Society for Industrial and Applied Mathematics, Jan. 2009
2009
Cited alongside, same era.
D. J. Bartholomew, M. Knott, and I. Moustaki, Latent variable models and factor analysis: A unified approach . John Wiley & Sons, 2011, vol. 904
2011
Cited alongside, same era.
B. Chen, S. He, Z. Li, and S. Zhang, “Maximum block improvement and polynomial optimization,” SIAM J. Optim. , vol. 22, no. 1, pp. 87–107, 2012
2012
Cited alongside, same era.
D. Park, A. Kyrillidis, C. Carmanis, and S. Sanghavi, “Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach,” in Artificial Intelligence and Statistics , 2017, pp. 65–74
2017
Later among the works it cites.
P. Jain and P. Kar, “Non-convex optimization for machine learning,” Foundations and Trends® in Machine Learning , vol. 10, no. 3-4, pp. 142–363, 2017
2017
Later among the works it cites.
Y. Sun, P. Babu, and D. P. Palomar, “Majorization-minimization algorithms in signal processing, communications, and machine learning,” IEEE Transactions on Signal Processing , vol. 65, no. 3, pp. 794–816, Feb. 2017
2017
Later among the works it cites.
D. Hong, L. Balzano, and J. A. Fessler, “Asymptotic performance of PCA for high-dimensional heteroscedastic data,” Journal of Multivariate Analysis , vol. 167, pp. 435–452, Sep. 2018
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2012
Cited alongside, same era.
M. Razaviyayn, M. Hong, and Z. Luo, “A unified convergence analysis of block successive minimization methods for nonsmooth optimization,” SIAM J. Optim. , vol. 23, no. 2, pp. 1126–53, 2013
2013
Cited alongside, same era.
A. Breloy, G. Ginolhac, F. Pascal, and P. Forster, “Clutter subspace estimation in low rank heterogeneous noise context,” IEEE Transactions on Signal Processing , vol. 63, no. 9, pp. 2173–2182, May 2015
2015
Cited alongside, same era.
Y. Cao and Y. Xie, “Poisson matrix recovery and completion,” IEEE Transactions on Signal Processing , vol. 64, no. 6, pp. 1609–1620, 2015
2015
Cited alongside, same era.
D. Passemier, Z. Li, and J. Yao, “On estimation of the noise variance in high dimensional probabilistic principal component analysis,” Journal of the Royal Statistical Society: Series B (Statistical Methodology) , vol. 79, no. 1, pp. 51–67, Dec. 2015
2015
Cited alongside, same era.
——, “Robust covariance matrix estimation in heterogeneous low rank context,” IEEE Transactions on Signal Processing , vol. 64, no. 22, pp. 5794–5806, Nov. 2016
2016
Cited alongside, same era.
Y. Sun, A. Breloy, P. Babu, D. P. Palomar, F. Pascal, and G. Ginolhac, “Low-complexity algorithms for low rank clutter parameters estimation in radar systems,” IEEE Transactions on Signal Processing , vol. 64, no. 8, pp. 1986–1998, Apr. 2016
2016
Cited alongside, same era.
O. Besson, “Bounds for a mixture of low-rank compound-gaussian and white gaussian noises,” IEEE Transactions on Signal Processing , vol. 64, no. 21, pp. 5723–5732, Nov. 2016
2016
Cited alongside, same era.
2018
Later among the works it cites.
G. Lerman and T. Maunu, “An overview of robust subspace recovery,” Proceedings of the IEEE , vol. 106, no. 8, pp. 1380–1410, 2018
2018
Later among the works it cites.
N. Vaswani, Y. Chi, and T. Bouwmans, “Rethinking PCA for modern data sets: Theory, algorithms, and applications [scanning the issue],” Proceedings of the IEEE , vol. 106, no. 8, pp. 1274–1276, 2018
2018
Later among the works it cites.
L. T. Liu, E. Dobriban, A. Singer et al. , “ e e PCA: high dimensional exponential family PCA,” Annals of Applied Statistics , vol. 12, no. 4, pp. 2121–2150, 2018
2018
Later among the works it cites.
D. Hong, L. Balzano, and J. A. Fessler, “Probabilistic PCA for heteroscedastic data,” in 8th IEEE Intl. Workshop on Computational Advances in Multi-Sensor Adaptive Processing , 2019, pp. 26–30
2019
Later among the works it cites.
2019
Later among the works it cites.
R. Y. Zhang, S. Sojoudi, and J. Lavaei, “Sharp restricted isometry bounds for the inexistence of spurious local minima in nonconvex matrix recovery,” Journal of Machine Learning Research , vol. 20, no. 114, pp. 1–34, 2019
2019
Later among the works it cites.
Y. Chi, Y. M. Lu, and Y. Chen, “Nonconvex optimization meets low-rank matrix factorization: An overview,” IEEE Transactions on Signal Processing , vol. 67, no. 20, pp. 5239–5269, 2019
2019
Later among the works it cites.
2019
Later among the works it cites.
2020
Later among the works it cites.
R. B. Abdallah, A. Breloy, M. N. E. Korso, and D. Lautru, “Bayesian signal subspace estimation with compound gaussian sources,” Signal Processing , vol. 167, p. 107310, Feb. 2020
2020
Later among the works it cites.
Y. Chen, Y. Chi, J. Fan, C. Ma, and Y. Yan, “Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization,” SIAM Journal of Optimization , 2020
2020
Later among the works it cites.
L. Ding and Y. Chen, “Leave-one-out approach for matrix completion: Primal and dual analysis,” IEEE Transactions on Information Theory , 2020
2020
Later among the works it cites.
2020
Later among the works it cites.