  Latent variable models for network data extract a summary of the relational
structure underlying an observed network. The simplest possible models
subdivide nodes of the network into clusters; the probability of a link between
any two nodes then depends only on their cluster assignment. Currently
available models can be classified by whether clusters are disjoint or are
allowed to overlap. These models can explain a "flat" clustering structure.
Hierarchical Bayesian models provide a natural approach to capture more complex
dependencies. We propose a model in which objects are characterised by a latent
feature vector. Each feature is itself partitioned into disjoint groups
(subclusters), corresponding to a second layer of hierarchy. In experimental
comparisons, the model achieves significantly improved predictive performance
on social and biological link prediction tasks. The results indicate that
models with a single layer hierarchy over-simplify real networks.
