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Pages 246-265
Received 01 Jan 2013
Accepted author version posted online: 17 Nov 2014
Published online:09 Mar 2016
 
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Latent space models (LSM) for network data rely on the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater their probability of being connected. In this article, we propose a variational inference approach to estimate the intractable posterior of the LSM. In many cases, different network views on the same set of nodes are available. It can therefore be useful to build a model able to jointly summarize the information given by all the network views. For this purpose, we introduce the latent space joint model (LSJM) that merges the information given by multiple network views assuming that the probability of a node being connected with other nodes in each network view is explained by a unique latent variable. This model is demonstrated on the analysis of two datasets: an excerpt of 50 girls from “Teenage Friends and Lifestyle Study” data at three time points and the Saccharomyces cerevisiae genetic and physical protein–protein interactions. Supplementary materials for this article are available online.

ACKNOWLEDGMENTS

The authors acknowledge the anonymous reviewers for helpful comments. This work was supported by Science Foundation funded Clique Research Cluster [grant number 08/SRC/I1407] and Insight Research Centre [grant number SFI/12/RC/2289]. Isabella Gollini’s research was also partially supported by the Natural Environment Research Council [Consortium on Risk in the Environment: Diagnostics, Integration, Benchmarking, Learning and Elicitation (CREDIBLE); grant number NE/J017450/1].

Additional information

Notes on contributors

Isabella Gollini

Isabella Gollini is Lecturer in Statistics, Department of Economics, Mathematics and Statistics, Birkbeck, University of London, England (E-mail: i.gollini@bbk.ac.uk). Thomas Brendan Murphy is Professor, School of Mathematical Sciences, Complex & Adaptive Systems Laboratory and Insight Research Centre, University College Dublin, Ireland (E-mail: brendan.murphy@ucd.ie).

Thomas Brendan Murphy

Isabella Gollini is Lecturer in Statistics, Department of Economics, Mathematics and Statistics, Birkbeck, University of London, England (E-mail: i.gollini@bbk.ac.uk). Thomas Brendan Murphy is Professor, School of Mathematical Sciences, Complex & Adaptive Systems Laboratory and Insight Research Centre, University College Dublin, Ireland (E-mail: brendan.murphy@ucd.ie).