  Traditional Relational Topic Models provide a way to discover the hidden
topics from a document network. Many theoretical and practical tasks, such as
dimensional reduction, document clustering, link prediction, benefit from this
revealed knowledge. However, existing relational topic models are based on an
assumption that the number of hidden topics is known in advance, and this is
impractical in many real-world applications. Therefore, in order to relax this
assumption, we propose a nonparametric relational topic model in this paper.
Instead of using fixed-dimensional probability distributions in its generative
model, we use stochastic processes. Specifically, a gamma process is assigned
to each document, which represents the topic interest of this document.
Although this method provides an elegant solution, it brings additional
challenges when mathematically modeling the inherent network structure of
typical document network, i.e., two spatially closer documents tend to have
more similar topics. Furthermore, we require that the topics are shared by all
the documents. In order to resolve these challenges, we use a subsampling
strategy to assign each document a different gamma process from the global
gamma process, and the subsampling probabilities of documents are assigned with
a Markov Random Field constraint that inherits the document network structure.
Through the designed posterior inference algorithm, we can discover the hidden
topics and its number simultaneously. Experimental results on both synthetic
and real-world network datasets demonstrate the capabilities of learning the
hidden topics and, more importantly, the number of topics.
