33,554 research outputs found
The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks
We consider the problem of analyzing timestamped relational events between a
set of entities, such as messages between users of an on-line social network.
Such data are often analyzed using static or discrete-time network models,
which discard a significant amount of information by aggregating events over
time to form network snapshots. In this paper, we introduce a block point
process model (BPPM) for continuous-time event-based dynamic networks. The BPPM
is inspired by the well-known stochastic block model (SBM) for static networks.
We show that networks generated by the BPPM follow an SBM in the limit of a
growing number of nodes. We use this property to develop principled and
efficient local search and variational inference procedures initialized by
regularized spectral clustering. We fit BPPMs with exponential Hawkes processes
to analyze several real network data sets, including a Facebook wall post
network with over 3,500 nodes and 130,000 events.Comment: To appear at The Web Conference 201
Statistical clustering of temporal networks through a dynamic stochastic block model
Statistical node clustering in discrete time dynamic networks is an emerging
field that raises many challenges. Here, we explore statistical properties and
frequentist inference in a model that combines a stochastic block model (SBM)
for its static part with independent Markov chains for the evolution of the
nodes groups through time. We model binary data as well as weighted dynamic
random graphs (with discrete or continuous edges values). Our approach,
motivated by the importance of controlling for label switching issues across
the different time steps, focuses on detecting groups characterized by a stable
within group connectivity behavior. We study identifiability of the model
parameters, propose an inference procedure based on a variational expectation
maximization algorithm as well as a model selection criterion to select for the
number of groups. We carefully discuss our initialization strategy which plays
an important role in the method and compare our procedure with existing ones on
synthetic datasets. We also illustrate our approach on dynamic contact
networks, one of encounters among high school students and two others on animal
interactions. An implementation of the method is available as a R package
called dynsbm
- …