Abstract
Interactions, either of molecules or people, are inherently dynamic, changing with time and context. Interactions have an inherent rhythm, often happening over a range of time scales. Temporal streams of interactions are commonly aggregated into dynamic networks for temporal analysis. Results of this analysis are greatly affected by the resolution at which the original data are aggregated. The mismatch between the inherent temporal scale of the underlying process and that at which the analysis is performed can obscure important insights and lead to wrong conclusions. In this chapter we describe the challenge of identifying the range of inherent temporal scales of a stream of interactions and of finding the dynamic network representation that matches those scales. We describe possible formalizations of the problem of identifying the inherent time scales of interactions and present some initial approaches at solving it, noting the advantages and limitations of these approaches. This is a nascent area of research and our goal is to highlight its importance and to establish a computational foundation for further investigations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ackerman, M., Ben-David, S., Loker, D.: Towards property-based classification of clustering paradigms. In: Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S., Culotta, A. (eds.) Neural Information Processing Systems, pp. 10–18 (2010). http://nips.cc/
Baldock, K., Memmott, J., Ruiz-Guajardo, J., Roze, D., Stone, G.S.: Daily temporal structure in african savanna flower visitation networks and consequences for network sampling. Ecology 92, 687–698 (2011)
Barabasi, A.L.: Bursts: The Hidden Pattern Behind Everything We Do. Dutton, New York (2010)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Barron, A.R., Rissanen, J., Yu, B.: The minimum description length principle in coding and modeling. IEEE Trans. Inf. Theor. 44(6), 2743–2760 (1998)
Ben-David, S., Ackerman, M.: Measures of clustering quality: a working set of axioms for clustering. Neural Information Processing Systems, pp. 121–128 (2008)
Bender-deMoll, S., McFarland, D.A.: The art and science of dynamic network visualization. J. Soc. Struct. 7(2), 1206–1241 (2006)
Blonder, B., Wey, T.W., Dornhaus, A., James, R., Sih, A.: Temporal dynamics and network analysis. In: Methods in Ecology and Evolution, pp. 958–972. Blackwell Publishing Ltd., Oxford (2012)
Butts, C.T.: An axiomatic approach to network complexity. J. Math. Sociol. 24, 273–301 (2000)
Caceres, R.S., Berger-Wolf, T., Grossman, R.: Temporal scale of processes in dynamic networks. In: IEEE 11th ICDM Workshops, pp. 925–932 (2011)
Chapanond, A., Krishnamoorthy, M., Yener, B.: Graph theoretic and spectral analysis of enron email data. Comput. Math. Organ. Theor. 11, 265–281 (2005)
Chung, F., Lu, L., Vu, V.: Spectra of random graphs with given expected degrees. Proc. Natl. Acad. Sci. 100(11), 6313–6318 (2003)
Clauset, A., Eagle, N.: Persistence and periodicity in a dynamic proximity network. In:Â DIMACS Workshop on Computational Methods for Dynamic Interaction Networks. DIMACS, Piscataway (2007)
Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51(4), 661–703 (2009)
Cross, P.C., Lloyd-Smith, J.O., Getz, W.M.: Disentangling association patterns in fission-fusion societies using african buffalo as an example. Anim. Behav. 69, 499–506 (2005)
Eagle, N., Pentland, A.: Reality mining: sensing complex social systems. Pers. Ubiquitous Comput. V10(4), 255–268 (2006)
Erdos, P., Renyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)
Feldmann, A., Gilbert, A.C., Willinger, W., Kurtz, T.: The changing nature of network traffic: scaling phenomena. Comput. Comm. Rev. 28, 5–29 (1998)
Fischhoff, I.R., Sundaresan, S.R., Cordingley, J., Larkin, H.M., Sellier, M.J., Rubenstein, D.I.: Social relationships and reproductive state influence leadership roles in movements of plains zebra, equus burchellii. Anim. Behav. 73(5), 825–831 (2007). doi:10.1016/j.anbehav.2006.10.012
Gao, Q., Li, M., Vitányi, P.M.B.: Applying MDL to learn best model granularity. Artif. Intell. 121(1–2), 1–29 (2000)
Hinde, R.A.: Interactions, relationships, and social structure. Man 11, 1–17 (1976)
Holme, P.: Network reachability of real-world contact sequences. Phys. Rev. E 71, 046119 (2004)
Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012) ArXiv e-prints (2011)
Hu, B., Rakthanmanon, T., Hao, Y., Evans, S., Lonardi, S., Keogh, E.J.: Discovering the intrinsic cardinality and dimensionality of time series using mdl. In: ICDM, pp. 1086–1091. IEEE Computer Society, Washington (2011)
Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabasi, A.L.: The large-scale organization of metabolic networks. Nature 407(6804), 651–654 (2000)
Karsai, M., Kivelä, M., Pan, R.K., Kaski, K., Kertész, J., Barabási, A.L., Saramäki, J.: Small but slow world: how network topology and burstiness slow down spreading. Phys. Rev. E 83, 025102 (2011)
Kempe, D., Kleinberg, J., Kumar, A.: Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci. 64(4), 820–842 (2002)
Keogh, E.J., Chu, S., Hart, D., Pazzani, M.J.: An online algorithm for segmenting time series. In: ICDM, pp. 289–296. IEEE Computer Society, Washington (2001)
Kivelä, M., Pan, R.K., Kaski, K., Kertész, J., Saramäki, J., Karsai, M.: Multiscale analysis of spreading in a large communication network. J. Stat. Mech. Theor. Exp. 3, 5 (2012)
Kleinberg, J.: An impossibility theorem for clustering. In: Advances in Neural Information Processing Systems, pp. 446–453 (2002)
Kleinberg, J.: Bursty and hierarchical structure in streams. Data Min. Knowl. Discov. 7(4), 373–397 (2003)
Krings, G., Karsai, M., Bernharsson, S., Blondel, V.D., Saramäki, J.: Effects of time window size and placement on the structure of aggregated networks. CoRR abs/1202.1145 (2012). http://arxiv.org/abs/1202.1145 ArXiv e-prints (2012)
Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.: Trawling the web for emerging cyber-communities. Comput. Netw. 31(11–16), 1481–1493 (1999)
Kumar, R., Novak, J., Tomkins, A.: Structure and evolution of online social networks. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 611–617. ACM, New York (2006)
Lahiri, M., Berger-Wolf, T.Y.: Structure prediction in temporal networks using frequent subgraphs. In: Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining, pp. 35–42. IEEE, New York (2007)
Lahiri, M., Maiya, A.S., Caceres, R.S., Habiba, Berger-Wolf, T.Y.: The impact of structural changes on predictions of diffusion in networks. In: Workshops Proceedings of the 8th IEEE International Conference on Data Mining, pp. 939–948. IEEE, New York (2008)
Meila, M.: Comparing clusterings: an axiomatic view. In: In ICML ’05: Proceedings of the 22nd international conference on Machine learning, pp. 577–584. ACM, New York (2005)
Miller, B.A., Bliss, N.T., Wolfe, P.J.: Toward signal processing theory for graphs and non-euclidean data. In: ICASSP, pp. 5414–5417. IEEE, New York (2010)
Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6(2–3), 161–180 (1995)
Molloy, M., Reed, B.: The size of the giant component of a random graph with a given degree sequence. Comb. Probab. Comput. 7(3), 295–305 (1998)
Moody, J., McFarland, D., Bender-deMoll, S.: Dynamic network visualization. Am. J. Sociol. 110(4), 1206–1241 (2005)
Morris, M., Kretzschmar, M.: Concurrent partnerships and transmission dynamics in networks. Soc. Netw. 17, 299–318 (1995)
Papadimitriou, S., Li, F., Kollios, G., Yu, P.S.: Time series compressibility and privacy. In: VLDB, pp. 459–470. VLDB Endowment, Vienna (2007)
Partridge, C., Cousins, D., Jackson, A.W., Krishnan, R., Saxena, T., Strayer, W.T.: Using signal processing to analyze wireless data traffic. In: Proceedings of the ACM Workshop on Wireless Security, pp. 67–76. ACM, New York (2002)
Pesaran, M.H., Timmermann, A.: Model instability and choice of observation window. Economics Working Paper Series 99–19, Department of Economics, UC San Diego, 1999
Riolo, C., Koopman, J., Chick, S.: Methods and measures for the description of epidemiologic contact networks. J. Urban Health 78, 446–457 (2001)
Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)
Rubenstein, D., Sundaresan, S., Fischhoff, I., Saltz, D.: Social networks in wild asses: comparing patterns and processes among populations, pp. 159–176. Martin-Luther-University Halle-Wittenberg, Halle (2007)
Sedley, D.: The stoic criterion of identity. Phronesis 27, 255–75 (1982)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)
Shetty, J., Adibi, J.: Enron email dataset. Institute, USC Information Sciences (2004). http://www.isi.edu/adibi/Enron/Enron.htm
Silk, J., Alberts, S., Altmann, J.: Social relationships among adult female baboons ( < i > papio cynocephalus < /i > ) ii. variation in the quality and stability of social bonds. Behav. Ecol. Sociobiol. 61(2), 197–204 (2006)
Sulo, R., Berger-Wolf, T., Grossman, R.: Meaningful selection of temporal resolution for dynamic networks. In: Proceedings of the 8th Workshop on Mining and Learning with Graphs, MLG ’10, pp. 127–136. ACM, New York (2010)
Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: KDD ’07: Proceedings of the 13th ACM SIGKDD on Knowledge Discovery and Data Mining, pp. 687–696. ACM, New York (2007)
Sundaresan, S.R., Fischhoff, I.R., Dushoff, J., Rubenstein, D.I.: Network metrics reveal differences in social organization between two fission-fusion species, grevy’s zebra and onager. Oecologia, 140–149 (2006)
Tanaka, Y., Iwamoto, K., Uehara, K.: Discovery of time-series motif from multi-dimensional data based on mdl principle. Mach. Learn. 58(2–3), 269–300 (2005)
Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: A framework for community identification in dynamic social networks. In: KDD ’07: Proceedings of the 13th ACM SIGKDD on Knowledge Discovery and Data Mining, pp. 717–726. ACM, New York (2007)
Yosef, N., Regev, A.: Impulse control: temporal dynamics in gene transcription. Cell 144, 886–896 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Caceres, R.S., Berger-Wolf, T. (2013). Temporal Scale of Dynamic Networks. In: Holme, P., Saramäki, J. (eds) Temporal Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36461-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-36461-7_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36460-0
Online ISBN: 978-3-642-36461-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)