Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
13th International Engine Congress 2026 | 24 + 25 February 2026

Meeting Place for the Powertrain and Sustainable Fuels Community

Take part as a speaker in the 13th International Engine Congress 2026, the Meeting Place for the Powertrain, and Sustainable Fuels Community for the exchange of experience. Submit a subject proposal online about our main subject areas: Passenger car engine technology, Commercial vehicle engine technology and Sustainable Fuels & Energy!
EXTENDED SEARCH
Log in
Top
Social Network Analysis and Mining
Published in:

01-12-2016 | Original Article

Block modelling in dynamic networks with non-homogeneous Poisson processes and exact ICL

Authors: Marco Corneli, Pierre Latouche, Fabrice Rossi

Published in: Social Network Analysis and Mining | Issue 1/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We develop a model in which interactions between nodes of a dynamic network are counted by non-homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity functions of the counting processes only depend on the clusters of nodes. In order to make inference tractable, we move to discrete time by partitioning the entire time horizon in which interactions are observed in fixed-length time sub-intervals. First, we derive an exact integrated classification likelihood criterion and maximize it relying on a greedy search approach. This allows to estimate the memberships to clusters and the number of clusters simultaneously. Then, a maximum likelihood estimator is developed to estimate nonparametrically the integrated intensities. We discuss the over-fitting problems of the model and propose a regularized version solving these issues. Experiments on real and simulated data are carried out in order to assess the proposed methodology.
previous article A computational approach for the experimental study of EU case law: analysis and implementation
next article A medical image retrieval scheme with relevance feedback through a medical social network

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Footnotes
1
In practice, the starting time of an interaction with a duration will be considered.
 
2
The model can easily be extended to the more general framework:
$$\begin{aligned} p\left( \pi _{kgu}|a_{kgu}, b_{kgu}\right) ={\text {Gamma}}(\pi _{kgu}|a_{kgu}, b_{kgu}). \end{aligned}$$
 
3
Hereafter, the “*” notation refers to the statistics after switching/merging.
 
4
The dimension of the vector \(\varvec{\omega }\) does not change.
 
5
More informations about the way the data were collected can be found in Isella et al. (2011) or visiting the website http://​www.​sociopatterns.​org/​datasets/​hypertext-2009-dynamic-contact-network/​.
 
Literature
Biernacki C, Celeux G, Govaert G (2000) Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Trans Pattern Anal Mach Intell 22(7):719–725CrossRef
Côme E, Latouche P (2015) Model selection and clustering in stochastic block models based on the exact integrated complete data likelihood. Stat Model 15(6):564–589MathSciNetCrossRef
Corneli M, Latouche P, Rossi F (2015) Modelling time evolving interactions in networks through a non stationary extension of stochastic block models. In: Pei J, Silvestri F, Tang J (eds) International conference on advances in social networks analysis and mining ASONAM 2015. IEEE/ACM, ACM, Paris, France, pp 1590–1591. https://​hal.​archives-ouvertes.​fr/​hal-01263540
Dubois C, Butts C, Smyth P (2013) Stochastic blockmodelling of relational event dynamics. In: International conference on artificial intelligence and statistics. Volume 31 of the Journal of Machine Learning Research Proceedings, pp 238–246
Goldenberg A, Zheng X, Fienberg SE, Airoldi EM (2009) A survey of statistical network models. Mach Learn 2(2):129–133CrossRefMATH
Guigourès R, Boullé M, Rossi F (2012) A triclustering approach for time evolving graphs. In: Co-clustering and applications, IEEE 12th international conference on data mining workshops (ICDMW 2012). Brussels, Belgium, pp 115–122
Isella L, Stehl J, Barrat A, Cattuto C, Pinton J, Van den Broeck W (2011) What’s in a crowd? Analysis of face-to-face behavioral networks. J Theor Biol 271(1):166–180CrossRef
Lorrain F, White H (1971) Structural equivalence of individuals in social networks. J Math Sociol 1:49–80CrossRef
Matias C, Rebafka T, Villers F (2015) Estimation and clustering in a semiparametric Poisson process stochastic block model for longitudinal networks, HAL (preprint)
Nouedoui L, Latouche P (2013) Bayesian non parametric inference of discrete valued networks. In: 21th European symposium on artificial neural networks, computational intelligence and machine learning (ESANN 2013). Bruges, Belgium, pp 291–296
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing, 3rd edn. Cambridge University Press, CambridgeMATH
Rand WM (1971) Objective criteria for the evaluation of clustering methods. J Am Stat Assoc 66(336):846–850CrossRef
Wasserman S, Faust K (1994) Social network analysis: methods and applications, vol 506. Cambridge University Press, CambridgeCrossRefMATH
White HC, Boorman S, Breiger R (1976) Social structure from multiple networks: I. Blockmodels of roles and positions. Am J Sociol 81(4):730–780CrossRef
Wyse J, Friel N, Latouche P (2014) Inferring structure in bipartite networks using the latent block model and exact icl. arXiv preprint arXiv:​1404.​2911
Xing EP, Fu W, Song L (2010) A state-space mixed membership blockmodel for dynamic network tomography. Ann Appl Stat 4(2):535–566MathSciNetCrossRefMATH
Xu KS, Hero III AO (2013) Dynamic stochastic blockmodels: statistical models for time-evolving networks. In: Proceedings of the 6th International Conference on Social Computing, Behavioral-Cultural Modeling, and Prediction, pp 201–210
Yang T, Chi Y, Zhu S, Gong Y, Jin R (2011) Detecting communities and their evolutions in dynamic social networks—a Bayesian approach. Mach Learn 82(2):157–189MathSciNetCrossRefMATH
Metadata
Title
Block modelling in dynamic networks with non-homogeneous Poisson processes and exact ICL
Authors
Marco Corneli
Pierre Latouche
Fabrice Rossi
Publication date
01-12-2016
Publisher
Springer Vienna
Published in
Social Network Analysis and Mining / Issue 1/2016
Print ISSN: 1869-5450
Electronic ISSN: 1869-5469
DOI
https://doi.org/10.1007/s13278-016-0368-3

Other articles of this Issue 1/2016

On finding small sets that influence large networks

  • Original Article

A new approach to role and position detection in networks

  • Original Article

Fast rumor source identification via random walks

  • Original Article

Identifying and validating personality traits-based homophilies for an egocentric network

  • Original Article

Large cultural networks and smart specialization: What is new in regional policy diagnostic analytics?

  • Original Article

Network topology and mean infection times

  • Original Article

Premium Partner

    Image Credits