  Traditional works on community detection from observations of information
cascade assume that a single adjacency matrix parametrizes all the observed
cascades. However, in reality the connection structure usually does not stay
the same across cascades. For example, different people have different topics
of interest, therefore the connection structure depends on the
information/topic content of the cascade. In this paper we consider the case
where we observe a sequence of noisy adjacency matrices triggered by
information/event with different topic distributions. We propose a novel latent
model using the intuition that a connection is more likely to exist between two
nodes if they are interested in similar topics, which are common with the
information/event. Specifically, we endow each node with two node-topic
vectors: an influence vector that measures how influential/authoritative they
are on each topic; and a receptivity vector that measures how
receptive/susceptible they are to each topic. We show how these two node-topic
structures can be estimated from observed adjacency matrices with theoretical
guarantee on estimation error, in cases where the topic distributions of the
information/event are known, as well as when they are unknown. Experiments on
synthetic and real data demonstrate the effectiveness of our model and superior
performance compared to state-of-the-art methods.
