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A review on low-rank models in data analysis
Born to be big: Data, graphs, and their entangled complexity
1. | Center for Computational Science, University of Miami, Miami, FL 33146, United States |
References:
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, Dealing with data (special issue),, Science, 331 (2011), 639.
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doi: 10.1161/CIRCULATIONAHA.114.014106. |
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E. Capobianco, Aliasing in gene feature detection by projective methods, J Bioinform Comput Biol, 7 (2009), 685-700.
doi: 10.1142/S0219720009004254. |
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N. V. Chavla, Data mining for imbalanced datasets: An overview, in Data Mining and Knowledge Discovery Handbook, Springer, (2005), 853-867. |
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L. Demetrius and T. Manke, Robustness and network evolution: An entropic principle, Phys A, 346 (2005), 682-696.
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D. L. Donoho, Compressed sensing, IEEE T. Inform. Theory, 52 (2006), 1289-1306.
doi: 10.1109/TIT.2006.871582. |
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Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications, Cambridge University Press, 2012.
doi: 10.1017/CBO9780511794308. |
[9] |
J. Fan, F. Han and H. Liu, Challenges of big data analysis, Nat Sci Rev, 1 (2014), 293-314.
doi: 10.1093/nsr/nwt032. |
[10] |
S. Garnerone, P. Giorda and P. Zanardi, Bipartite quantum states and random complex networks, New J Phys, 14 (2012), 013011.
doi: 10.1088/1367-2630/14/1/013011. |
[11] |
R. Gens and P. Domingos, Deep Symmetry Networks, Advances in Neural Information Processing Systems, 2014. |
[12] |
U. Grenander, Probability and Statistics: The Harald Cramér Volume, Wiley, 1959. |
[13] |
S. Havlin, E. Lopez, S. Buldyrev and H. E. Stanley, Anomalous conductance and diffusion in complex networks, Diff Fundam, 2 (2005), 1-11. |
[14] |
K. M. Lee, B. Mina and K. Gohb, Towards real-world complexity: An introduction to multiplex networks, Eur. Phys. J. B, 88 (2015), p48.
doi: 10.1140/epjb/e2015-50742-1. |
[15] |
J. Leskovec, K. J. Lang, A. Dasgupta and M. W. Mahoney, Statistical properties of community structure in large social and information networks, Prooc. WWW 17th Int Conf, (2008), 695-704.
doi: 10.1145/1367497.1367591. |
[16] |
B. G. Lindsay, Mixture models: theory, geometry and applications, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995). |
[17] |
R. Lopez-Ruiz, H. L. Mancini and X. Calbert, A statistical measure of complexity, Concepts and Recent Advances in Generalized Information Measures and Statistics, (2013), 147-168.
doi: 10.2174/9781608057603113010012. |
[18] |
C. Lynch, Big Data: How do your data grow?, Nature, 455 (2008), 28-29.
doi: 10.1038/455028a. |
[19] |
E. Marras, A. Travaglione and E. Capobianco, Sub-modular resolution analysis by network mixture models, Stat Appl Genet Mol Biol, 9 (2010), Art 19, 43pp.
doi: 10.2202/1544-6115.1523. |
[20] |
A. Montanari, Computational implications of reducing data to sufficient statistics, Electron. J. Statist, 9 (2015), 2370-2390.
doi: 10.1214/15-EJS1059. |
[21] |
M. E. J. Newman, Modularity and community structure in networks, PNAS, 103 (2006), 8577-8582.
doi: 10.1073/pnas.0601602103. |
[22] |
M. E. J. Newman and E. A. Leicht, Mixture models and exploratory analysis in networks, PNAS, 104 (2007), 9564-9569.
doi: 10.1073/pnas.0610537104. |
[23] |
V. Nicosia, M. Valencia, M. Chavez, A. Diaz-Guilera and V. Latora, Remote synchronization reveals network symmetries and functional modules, Phys Rev Lett, 110 (2013), 174102.
doi: 10.1103/PhysRevLett.110.174102. |
[24] |
B. Olshausen, Sparse Codes and Spikes, in Probabilistic Models of the Brain: Perception and Neural Function, (eds. R.P.N. Rao, B.A. Olshausen and M.S. Lewicki), MIT Press, 2002. |
[25] |
R. Orus, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann Phys, 349 (2014), 117-158.
doi: 10.1016/j.aop.2014.06.013. |
[26] |
J. J. Ramasco and M. Mungan, Inversion method for content-based networks, Phys Rev E, 77 (2008), 036122, 12 pp.
doi: 10.1103/PhysRevE.77.036122. |
[27] |
J. J. Slotine and Y. Y. Liu, Complex Networks: The missing link, Nat Phys, 8 (2012), 512-513.
doi: 10.1038/nphys2342. |
[28] |
J. W. Vaupel and A. I Yashin, Heterogeneity's ruses: Some surprising effects of selection on population dynamics, Amer Statist, 39 (1985), 176-185.
doi: 10.2307/2683925. |
show all references
References:
[1] |
, Dealing with data (special issue),, Science, 331 (2011), 639.
|
[2] |
R. B. Altman and E. A. Ashley, Using "Big Data" to dissect clinical heterogeneity, Circulation, 131 (2015), 232-233.
doi: 10.1161/CIRCULATIONAHA.114.014106. |
[3] |
E. J. Candes, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE T. Inform. Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. Capobianco, Aliasing in gene feature detection by projective methods, J Bioinform Comput Biol, 7 (2009), 685-700.
doi: 10.1142/S0219720009004254. |
[5] |
N. V. Chavla, Data mining for imbalanced datasets: An overview, in Data Mining and Knowledge Discovery Handbook, Springer, (2005), 853-867. |
[6] |
L. Demetrius and T. Manke, Robustness and network evolution: An entropic principle, Phys A, 346 (2005), 682-696.
doi: 10.1016/j.physa.2004.07.011. |
[7] |
D. L. Donoho, Compressed sensing, IEEE T. Inform. Theory, 52 (2006), 1289-1306.
doi: 10.1109/TIT.2006.871582. |
[8] |
Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications, Cambridge University Press, 2012.
doi: 10.1017/CBO9780511794308. |
[9] |
J. Fan, F. Han and H. Liu, Challenges of big data analysis, Nat Sci Rev, 1 (2014), 293-314.
doi: 10.1093/nsr/nwt032. |
[10] |
S. Garnerone, P. Giorda and P. Zanardi, Bipartite quantum states and random complex networks, New J Phys, 14 (2012), 013011.
doi: 10.1088/1367-2630/14/1/013011. |
[11] |
R. Gens and P. Domingos, Deep Symmetry Networks, Advances in Neural Information Processing Systems, 2014. |
[12] |
U. Grenander, Probability and Statistics: The Harald Cramér Volume, Wiley, 1959. |
[13] |
S. Havlin, E. Lopez, S. Buldyrev and H. E. Stanley, Anomalous conductance and diffusion in complex networks, Diff Fundam, 2 (2005), 1-11. |
[14] |
K. M. Lee, B. Mina and K. Gohb, Towards real-world complexity: An introduction to multiplex networks, Eur. Phys. J. B, 88 (2015), p48.
doi: 10.1140/epjb/e2015-50742-1. |
[15] |
J. Leskovec, K. J. Lang, A. Dasgupta and M. W. Mahoney, Statistical properties of community structure in large social and information networks, Prooc. WWW 17th Int Conf, (2008), 695-704.
doi: 10.1145/1367497.1367591. |
[16] |
B. G. Lindsay, Mixture models: theory, geometry and applications, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995). |
[17] |
R. Lopez-Ruiz, H. L. Mancini and X. Calbert, A statistical measure of complexity, Concepts and Recent Advances in Generalized Information Measures and Statistics, (2013), 147-168.
doi: 10.2174/9781608057603113010012. |
[18] |
C. Lynch, Big Data: How do your data grow?, Nature, 455 (2008), 28-29.
doi: 10.1038/455028a. |
[19] |
E. Marras, A. Travaglione and E. Capobianco, Sub-modular resolution analysis by network mixture models, Stat Appl Genet Mol Biol, 9 (2010), Art 19, 43pp.
doi: 10.2202/1544-6115.1523. |
[20] |
A. Montanari, Computational implications of reducing data to sufficient statistics, Electron. J. Statist, 9 (2015), 2370-2390.
doi: 10.1214/15-EJS1059. |
[21] |
M. E. J. Newman, Modularity and community structure in networks, PNAS, 103 (2006), 8577-8582.
doi: 10.1073/pnas.0601602103. |
[22] |
M. E. J. Newman and E. A. Leicht, Mixture models and exploratory analysis in networks, PNAS, 104 (2007), 9564-9569.
doi: 10.1073/pnas.0610537104. |
[23] |
V. Nicosia, M. Valencia, M. Chavez, A. Diaz-Guilera and V. Latora, Remote synchronization reveals network symmetries and functional modules, Phys Rev Lett, 110 (2013), 174102.
doi: 10.1103/PhysRevLett.110.174102. |
[24] |
B. Olshausen, Sparse Codes and Spikes, in Probabilistic Models of the Brain: Perception and Neural Function, (eds. R.P.N. Rao, B.A. Olshausen and M.S. Lewicki), MIT Press, 2002. |
[25] |
R. Orus, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann Phys, 349 (2014), 117-158.
doi: 10.1016/j.aop.2014.06.013. |
[26] |
J. J. Ramasco and M. Mungan, Inversion method for content-based networks, Phys Rev E, 77 (2008), 036122, 12 pp.
doi: 10.1103/PhysRevE.77.036122. |
[27] |
J. J. Slotine and Y. Y. Liu, Complex Networks: The missing link, Nat Phys, 8 (2012), 512-513.
doi: 10.1038/nphys2342. |
[28] |
J. W. Vaupel and A. I Yashin, Heterogeneity's ruses: Some surprising effects of selection on population dynamics, Amer Statist, 39 (1985), 176-185.
doi: 10.2307/2683925. |
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