Abstract
In recent years network analysis have become the focus of much research
in many fields including biology, communication studies, economics,
information science, organizational studies, and social psychology.
Communities or clusters of highly connected actors form an essential
feature in the structure of several empirical networks. Spectral clustering
is a popular and computationally feasible method to discover these
communities.
The Stochastic Block Model is a social network model with well defined
communities. This talk will give conditions for spectral clustering to
correctly estimate the community membership of nearly all nodes. These
asymptotic results are the first clustering results that allow the number
of clusters in the model to grow with the number of nodes, hence the name
high-dimensional. Moreover, I will present on-going work on directed
spectral clustering for networks whose edges are directed, including the
enron and c. elegans network data as examples.