  Latent space models (LSM) for network data were introduced by Hoff et al.
(2002) under 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 paper we propose a variational Bayes 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
summarise 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: the
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.
