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

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

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.
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
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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.

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E. Capobianco, Aliasing in gene feature detection by projective methods,, J Bioinform Comput Biol, 7 (2009), 685. 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, (2005), 853.

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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.

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D. L. Donoho, Compressed sensing,, IEEE T. Inform. Theory, 52 (2006), 1289. 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. 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). 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.

[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.

[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.

[16]

B. G. Lindsay, Mixture models: theory, geometry and applications,, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995)., 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. doi: 10.2174/9781608057603113010012.

[18]

C. Lynch, Big Data: How do your data grow?,, Nature, 455 (2008), 28. 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). doi: 10.2202/1544-6115.1523.

[20]

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

[21]

M. E. J. Newman, Modularity and community structure in networks,, PNAS, 103 (2006), 8577. 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. 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). doi: 10.1103/PhysRevLett.110.174102.

[24]

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

[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.

[26]

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

[27]

J. J. Slotine and Y. Y. Liu, Complex Networks: The missing link,, Nat Phys, 8 (2012), 512. 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. 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. 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. doi: 10.1109/TIT.2005.862083.

[4]

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

[5]

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

[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.

[7]

D. L. Donoho, Compressed sensing,, IEEE T. Inform. Theory, 52 (2006), 1289. 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. 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). 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.

[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.

[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.

[16]

B. G. Lindsay, Mixture models: theory, geometry and applications,, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995)., 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. doi: 10.2174/9781608057603113010012.

[18]

C. Lynch, Big Data: How do your data grow?,, Nature, 455 (2008), 28. 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). doi: 10.2202/1544-6115.1523.

[20]

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

[21]

M. E. J. Newman, Modularity and community structure in networks,, PNAS, 103 (2006), 8577. 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. 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). doi: 10.1103/PhysRevLett.110.174102.

[24]

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

[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.

[26]

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

[27]

J. J. Slotine and Y. Y. Liu, Complex Networks: The missing link,, Nat Phys, 8 (2012), 512. 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. doi: 10.2307/2683925.

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