American Institute of Mathematical Sciences

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July  2016, 1(2&3): 163-169. doi: 10.3934/bdia.2016002

Born to be big: Data, graphs, and their entangled complexity

Enrico Capobianco 1,

1. 

Center for Computational Science, University of Miami, Miami, FL 33146, United States

Received  May 2016 Revised  July 2016 Published  August 2016

Big Data and Big Graphs have become landmarks of current cross-border research, destined to remain so for long time. While we try to optimize the ability of assimilating both, novel methods continue to inspire new applications, and vice versa.Clearly these two big things, data and graphs, are connected, but can we ensure management of their complexities, computational efficiency, robust inference? Critical bridging features are addressed here to identify grand challenges and bottlenecks.
Keywords: Complexity, heterogeneity, symmetries., dimensionality, entanglement, graph connectivity.
Mathematics Subject Classification: Primary: 68Qxx; Secondary: 81P4.
Citation: Enrico Capobianco. Born to be big: Data, graphs, and their entangled complexity. Big Data & Information Analytics, 2016, 1 (2&3) : 163-169. doi: 10.3934/bdia.2016002
References:
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Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications,, Cambridge University Press, (2012).  doi: 10.1017/CBO9780511794308.  Google Scholar

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J. Fan, F. Han and H. Liu, Challenges of big data analysis,, Nat Sci Rev, 1 (2014), 293.  doi: 10.1093/nsr/nwt032.  Google Scholar

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S. Garnerone, P. Giorda and P. Zanardi, Bipartite quantum states and random complex networks,, New J Phys, 14 (2012).  doi: 10.1088/1367-2630/14/1/013011.  Google Scholar

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R. Gens and P. Domingos, Deep Symmetry Networks,, Advances in Neural Information Processing Systems, (2014).   Google Scholar

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S. Havlin, E. Lopez, S. Buldyrev and H. E. Stanley, Anomalous conductance and diffusion in complex networks,, Diff Fundam, 2 (2005), 1.   Google Scholar

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K. M. Lee, B. Mina and K. Gohb, Towards real-world complexity: An introduction to multiplex networks,, Eur. Phys. J. B, 88 (2015).  doi: 10.1140/epjb/e2015-50742-1.  Google Scholar

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B. G. Lindsay, Mixture models: theory, geometry and applications,, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995)., 5 (1995).   Google Scholar

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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.  doi: 10.2174/9781608057603113010012.  Google Scholar

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C. Lynch, Big Data: How do your data grow?,, Nature, 455 (2008), 28.  doi: 10.1038/455028a.  Google Scholar

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E. Marras, A. Travaglione and E. Capobianco, Sub-modular resolution analysis by network mixture models,, Stat Appl Genet Mol Biol, 9 (2010).  doi: 10.2202/1544-6115.1523.  Google Scholar

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A. Montanari, Computational implications of reducing data to sufficient statistics,, Electron. J. Statist, 9 (2015), 2370.  doi: 10.1214/15-EJS1059.  Google Scholar

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M. E. J. Newman, Modularity and community structure in networks,, PNAS, 103 (2006), 8577.  doi: 10.1073/pnas.0601602103.  Google Scholar

[22]

M. E. J. Newman and E. A. Leicht, Mixture models and exploratory analysis in networks,, PNAS, 104 (2007), 9564.  doi: 10.1073/pnas.0610537104.  Google Scholar

[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).  doi: 10.1103/PhysRevLett.110.174102.  Google Scholar

[24]

B. Olshausen, Sparse Codes and Spikes,, in Probabilistic Models of the Brain: Perception and Neural Function, (2002).   Google Scholar

[25]

R. Orus, A practical introduction to tensor networks: Matrix product states and projected entangled pair states,, Ann Phys, 349 (2014), 117.  doi: 10.1016/j.aop.2014.06.013.  Google Scholar

[26]

J. J. Ramasco and M. Mungan, Inversion method for content-based networks,, Phys Rev E, 77 (2008).  doi: 10.1103/PhysRevE.77.036122.  Google Scholar

[27]

J. J. Slotine and Y. Y. Liu, Complex Networks: The missing link,, Nat Phys, 8 (2012), 512.  doi: 10.1038/nphys2342.  Google Scholar

[28]

J. W. Vaupel and A. I Yashin, Heterogeneity's ruses: Some surprising effects of selection on population dynamics,, Amer Statist, 39 (1985), 176.  doi: 10.2307/2683925.  Google Scholar

show all references

References:
[1]

, Dealing with data (special issue),, Science, 331 (2011), 639.   Google Scholar

[2]

R. B. Altman and E. A. Ashley, Using "Big Data" to dissect clinical heterogeneity,, Circulation, 131 (2015), 232.  doi: 10.1161/CIRCULATIONAHA.114.014106.  Google Scholar

[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.  doi: 10.1109/TIT.2005.862083.  Google Scholar

[4]

E. Capobianco, Aliasing in gene feature detection by projective methods,, J Bioinform Comput Biol, 7 (2009), 685.  doi: 10.1142/S0219720009004254.  Google Scholar

[5]

N. V. Chavla, Data mining for imbalanced datasets: An overview,, in Data Mining and Knowledge Discovery Handbook, (2005), 853.   Google Scholar

[6]

L. Demetrius and T. Manke, Robustness and network evolution: An entropic principle,, Phys A, 346 (2005), 682.  doi: 10.1016/j.physa.2004.07.011.  Google Scholar

[7]

D. L. Donoho, Compressed sensing,, IEEE T. Inform. Theory, 52 (2006), 1289.  doi: 10.1109/TIT.2006.871582.  Google Scholar

[8]

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications,, Cambridge University Press, (2012).  doi: 10.1017/CBO9780511794308.  Google Scholar

[9]

J. Fan, F. Han and H. Liu, Challenges of big data analysis,, Nat Sci Rev, 1 (2014), 293.  doi: 10.1093/nsr/nwt032.  Google Scholar

[10]

S. Garnerone, P. Giorda and P. Zanardi, Bipartite quantum states and random complex networks,, New J Phys, 14 (2012).  doi: 10.1088/1367-2630/14/1/013011.  Google Scholar

[11]

R. Gens and P. Domingos, Deep Symmetry Networks,, Advances in Neural Information Processing Systems, (2014).   Google Scholar

[12]

U. Grenander, Probability and Statistics: The Harald Cramér Volume,, Wiley, (1959).   Google Scholar

[13]

S. Havlin, E. Lopez, S. Buldyrev and H. E. Stanley, Anomalous conductance and diffusion in complex networks,, Diff Fundam, 2 (2005), 1.   Google Scholar

[14]

K. M. Lee, B. Mina and K. Gohb, Towards real-world complexity: An introduction to multiplex networks,, Eur. Phys. J. B, 88 (2015).  doi: 10.1140/epjb/e2015-50742-1.  Google Scholar

[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.  doi: 10.1145/1367497.1367591.  Google Scholar

[16]

B. G. Lindsay, Mixture models: theory, geometry and applications,, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995)., 5 (1995).   Google Scholar

[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.  doi: 10.2174/9781608057603113010012.  Google Scholar

[18]

C. Lynch, Big Data: How do your data grow?,, Nature, 455 (2008), 28.  doi: 10.1038/455028a.  Google Scholar

[19]

E. Marras, A. Travaglione and E. Capobianco, Sub-modular resolution analysis by network mixture models,, Stat Appl Genet Mol Biol, 9 (2010).  doi: 10.2202/1544-6115.1523.  Google Scholar

[20]

A. Montanari, Computational implications of reducing data to sufficient statistics,, Electron. J. Statist, 9 (2015), 2370.  doi: 10.1214/15-EJS1059.  Google Scholar

[21]

M. E. J. Newman, Modularity and community structure in networks,, PNAS, 103 (2006), 8577.  doi: 10.1073/pnas.0601602103.  Google Scholar

[22]

M. E. J. Newman and E. A. Leicht, Mixture models and exploratory analysis in networks,, PNAS, 104 (2007), 9564.  doi: 10.1073/pnas.0610537104.  Google Scholar

[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).  doi: 10.1103/PhysRevLett.110.174102.  Google Scholar

[24]

B. Olshausen, Sparse Codes and Spikes,, in Probabilistic Models of the Brain: Perception and Neural Function, (2002).   Google Scholar

[25]

R. Orus, A practical introduction to tensor networks: Matrix product states and projected entangled pair states,, Ann Phys, 349 (2014), 117.  doi: 10.1016/j.aop.2014.06.013.  Google Scholar

[26]

J. J. Ramasco and M. Mungan, Inversion method for content-based networks,, Phys Rev E, 77 (2008).  doi: 10.1103/PhysRevE.77.036122.  Google Scholar

[27]

J. J. Slotine and Y. Y. Liu, Complex Networks: The missing link,, Nat Phys, 8 (2012), 512.  doi: 10.1038/nphys2342.  Google Scholar

[28]

J. W. Vaupel and A. I Yashin, Heterogeneity's ruses: Some surprising effects of selection on population dynamics,, Amer Statist, 39 (1985), 176.  doi: 10.2307/2683925.  Google Scholar

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