Bilinear generalized approximate message passing - Part II: Applications

IEEE Transactions on Signal Processing

Volumn 62, Issue 22, 2014, Pages 5854-5867

  Parker, Jason T ^a   Schniter, Philip ^b   Cevher, Volkan ^c  

^a AIR FORCE RESEARCH LABORATORY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

^c EPFL   (Switzerland)

Author keywords

Approximate message passing; belief propagation; bilinear estimation; dictionary learning robust principal components analysis; matrix completion; matrix factorization

Indexed keywords

BELIEF PROPAGATION; MATRIX COMPLETION; MATRIX FACTORIZATIONS; ROBUST PRINCIPAL COMPONENTS;

EID: 84908432907     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2014.2357773     Document Type: Article

References (28)

1. J. T. Parker, P. Schniter, and V. Cevher, "Bilinear generalized approximate message passing-Part I: Derivation," IEEE Trans. Signal Process., vol. 62, no. 22, pp. 5839-5853, 2014.
2. P. Schniter and V. Cevher, "Approximate message passing for bilinear models," in Proc. Workshop Signal Process. Adapt. Sparse Struct. Repr. (SPARS), Edinburgh, Scotland, Jun. 2011, p. 68.
3. P. Schniter, J. T. Parker, and V. Cevher, "Bilinear generalized approximate message passing (BiG-AMP) for matrix recovery problems," presented at the Inf. Theory Appl. Workshop (ITA), La Jolla, CA, USA, Feb. 2012.
4. J. T. Parker and P. Schniter, "Bilinear generalized approximate message passing (BiG-AMP) for matrix completion," presented at the Asilomar Conf., Pacific Grove, CA, USA, Nov. 2012.
5. D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing," Proc. Nat. Acad. Sci., vol. 106, no. 45, pp. 18 914-18 919, Nov. 2009.
6. D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing: I. Motivation and construction," in Proc. Inf. Theory Workshop, Cairo, Egypt, Jan. 2010, pp. 1-5.
7. S. Rangan, "Generalized approximate message passing for estimation with randomlinearmixing," in Proc. IEEE Int. Symp. Inf. Theory, Saint Petersburg, Russia, Aug. 2011, pp. 2168-2172.
8. E. J. Candés and Y. Plan, "Matrix completion with noise," Proc. IEEE, vol. 98, no. 6, pp. 925-936, Jun. 2010.
9. M. E. Tipping and C. M. Bishop, "Probabilistic principal component analysis," J. Roy. Statist. Soc. B, vol. 61, no. 3, pp. 611-622, 1999.
10. Y. Lim and Y. Teh, "Variational Bayesian approach to movie rating prediction," in Proc. KDD Cup Workshop, 2007, pp. 15-21, Citeseer.
11. R. Salakhutdinov and A. Mnih, "Probabilistic matrix factorization," in Proc. Neural Inf. Process. Syst. Conf., Vancouver, BC, Dec. 2008, pp. 1257-1264.
12. N. D. Lawrence and R. Urtasun, "Non-linear matrix factorization with Gaussian processes," in Proc. Int. Conf. Mach. Learning, Montreal, QC, Canada, Jun. 2009, pp. 601-608.
13. Z. Wen, W. Yin, and Y. Zhang, "Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm," Math. Programm. Comput. vol. 4, pp. 333-361, 2012 [Online]. Available: http://dx.doi.org/10.1007/s12532-012-0044-1
14. S. D. Babacan, M. Luessi, R. Molina, and A. K. Katsaggelos, "Sparse Bayesian methods for low-rankmatrix estimation," IEEE Trans. Signal Process., vol. 60, no. 8, pp. 3964-3977, Aug. 2012.
15. J. P. Vila and P. Schniter, "Expectation-maximization Gaussian-mixture approximate message passing," IEEE Trans. Signal Process., vol. 61, no. 19, pp. 4658-4672, Oct. 2013.
16. P. Stoica and Y. Selen, "Model-order selection: A review of information criterion rules," IEEE Signal Process. Mag., vol. 21, no. 4, pp. 36-47, Jul. 2004.
17. G.Marjanovic and V. Solo, "On optimization and matrix completion," IEEE Trans. Signal Process., vol. 60, no. 11, pp. 5714-5724, 2012.
18. Z. Lin, M. Chen, L. Wu, and Y. Ma, "The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices," 2010, arXiv preprint: 1009.5055 [Online]. Available: http://arxiv.org/abs/1009.5055
19. L. Balzano, R. Nowak, and B. Recht, "Online identification and tracking of subspaces from highly incomplete information," in Proc. Allerton Conf. Commun. Control Comput., Sep. 2010, pp. 704-711.
20. A. Kyrillidis and V. Cevher, "Matrix recipes for hard thresholding methods," J. Math. Imag. Vis., vol. 48, pp. 235-265, 2014.
21. E. J. Candès, X. Li, Y. Ma, and J.Wright, "Robust principal component analysis?," J. ACM vol. 58, no. 3, pp. 11:1-11:37, Jun. 2011 [Online]. Available: http://doi.acm.org/10.1145/1970392.1970395
22. J. He, L. Balzano, and J. Lui, "Online robust subspace tracking from partial information," 2011, arXiv preprint: 1109.3827 [Online]. Available: http://arxiv.org/abs/1109.3827
23. R. Rubinstein, A. Bruckstein, and M. Elad, "Dictionaries for sparse representation modeling," Proc. IEEE, vol. 98, no. 6, pp. 1045-1057, 2010.
24. D. A. Spielman, H. Wang, and J. Wright, "Exact recovery of sparselyused dictionaries," in JMLR: Workshop Conf. Proc. 25th Annu. Conf. Learn. Theory, 2012, vol. 23, pp. 37.1-37.18 [Online]. Available: http://jmlr.org/proceedings/papers/v23/spielman12/spielman12.pdf
25. J. Vila, P. Schniter, and J. Meola, "Hyperspectral image unmixing via bilinear generalized approximate message passing," Proc. SPIE, vol. 8743, no. 87430Y, p. 9, 2013.
26. M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4311-4322, 2006.
27. J.Mairal, F. Bach, J. Ponce, and G. Sapiro, "Online learning for matrix factorization and sparse coding," J. Mach. Learn. Res., vol. 11, pp. 19-60, 2010.
28. F. Krzakala, M. Mézard, and L. Zdeborová, "Phase diagram and approximate message passing for blind calibration and dictionary learning," in Proc. IEEE Int. Symp. Inf. Theory, 2013, pp. 659-663.