  We face network data from various sources, such as protein interactions and
online social networks. A critical problem is to model network interactions and
identify latent groups of network nodes. This problem is challenging due to
many reasons. For example, the network nodes are interdependent instead of
independent of each other, and the data are known to be very noisy (e.g.,
missing edges). To address these challenges, we propose a new relational model
for network data, Sparse Matrix-variate Gaussian process Blockmodel (SMGB). Our
model generalizes popular bilinear generative models and captures nonlinear
network interactions using a matrix-variate Gaussian process with latent
membership variables. We also assign sparse prior distributions on the latent
membership variables to learn sparse group assignments for individual network
nodes. To estimate the latent variables efficiently from data, we develop an
efficient variational expectation maximization method. We compared our
approaches with several state-of-the-art network models on both synthetic and
real-world network datasets. Experimental results demonstrate SMGBs outperform
the alternative approaches in terms of discovering latent classes or predicting
unknown interactions.
