Born to be Big: data, graphs, and their entangled complexity

Enrico Capobianco; Enrico Capobianco

doi:10.3934/bdia.2016002

Big Data and Information Analytics

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

Previous Article Next Article

Born to be Big: data, graphs, and their entangled complexity

Enrico Capobianco

Center for Computational Science, University of Miami, Miami, FL 33146, USA

Received: 01 May 2016 Revised: 01 July 2016 Published: 01 July 2016
Primary: 68Qxx; Secondary: 81P40

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.
- Complexity,
- dimensionality,
- heterogeneity,
- graph connectivity,
- entanglement,
- symmetries
Citation: Enrico Capobianco. 2016: Born to be Big: data, graphs, and their entangled complexity, Big Data and Information Analytics, 1(2&3): 163-169. doi: 10.3934/bdia.2016002

Related Papers:

Abstract

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.

References

[1]	Dealing with data (special issue), Science, 331 (2011), 639–806.
[2]	Altman R. B., Ashley E. A. (2015) Using "Big Data" to dissect clinical heterogeneity. Circulation 131: 232-233.
[3]	Candes E. J., Romberg J., Tao T. (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE T. Inform. Theory 52: 489-509.
[4]	Capobianco E. (2009) Aliasing in gene feature detection by projective methods. J Bioinform Comput Biol 7: 685-700.
[5]	N. V. Chavla, Data mining for imbalanced datasets: An overview, in Data Mining and Knowledge Discovery Handbook, Springer, (2005), 853–867.
[6]	Demetrius L., Manke T. (2005) Robustness and network evolution: An entropic principle. Phys A 346: 682-696.
[7]	Donoho D. L. (2006) Compressed sensing. IEEE T. Inform. Theory 52: 1289-1306.
[8]	Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications, Cambridge University Press, 2012. 10.1017/CBO9780511794308 MR2961961
[9]	Fan J., Han F., Liu H. (2014) Challenges of big data analysis. Nat Sci Rev 1: 293-314.
[10]	S. Garnerone, P. Giorda and P. Zanardi, Bipartite quantum states and random complex networks, New J Phys, 14 (2012), 013011. 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]	Havlin S., Lopez E., Buldyrev S., Stanley H. E. (2005) Anomalous conductance and diffusion in complex networks. Diff Fundam 2: 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. 10.1140/epjb/e2015-50742-1
[15]	Leskovec J., Lang K. J., Dasgupta A., Mahoney M. W. (2008) Statistical properties of community structure in large social and information networks. Prooc. WWW 17th Int Conf : 695-704.
[16]	B. G. Lindsay, Mixture models: theory, geometry and applications, NSF-CBMS Regional Conf. Ser. Prob. Stat 5 (1995).
[17]	Lopez-Ruiz R., Mancini H. L., Calbert X. (2013) A statistical measure of complexity. Concepts and Recent Advances in Generalized Information Measures and Statistics : 147-168.
[18]	Lynch C. (2008) Big Data: How do your data grow?. Nature 455: 28-29.
[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. 10.2202/1544-6115.1523 MR2721699
[20]	Montanari A. (2015) Computational implications of reducing data to sufficient statistics. Electron. J. Statist 9: 2370-2390.
[21]	Newman M. E. J. (2006) Modularity and community structure in networks. PNAS 103: 8577-8582.
[22]	Newman M. E. J., Leicht E. A. (2007) Mixture models and exploratory analysis in networks. PNAS 104: 9564-9569.
[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. 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]	Orus R. (2014) A practical introduction to tensor networks: Matrix product states and projected entangled pair states. Ann Phys 349: 117-158.
[26]	J. J. Ramasco and M. Mungan, Inversion method for content-based networks, Phys Rev E, 77 (2008), 036122, 12 pp. 10.1103/PhysRevE.77.036122 MR2495435
[27]	Slotine J. J., Liu Y. Y. (2012) Complex Networks: The missing link. Nat Phys 8: 512-513.
[28]	Vaupel J. W., I Yashin A. (1985) Heterogeneity's ruses: Some surprising effects of selection on population dynamics. Amer Statist 39: 176-185.

Reader Comments

Your name:*

Email:*
© 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)