1202.0425 (Alcides Viamontes Esquivel et al.)

Comparing network covers using mutual information    [PDF]

Alcides Viamontes Esquivel, Martin Rosvall

In network science, researchers often use mutual information to understand
the difference between network partitions produced by community detection
methods. Here we extend the use of mutual information to covers, that is, the
cases where a node can belong to more than one module. In our proposed
solution, the underlying stochastic process used to compare partitions is
extended to deal with covers, and the random variables of the new process are
simply fed into the usual definition of mutual information. With partitions,
our extended process behaves exactly as the conventional approach for
partitions, and thus, the mutual information values obtained are the same. We
also describe how to perform sampling and do error estimation for our extended
process, as both are necessary steps for a practical application of this
measure. The stochastic process that we define here is not only applicable to
networks, but can also be used to compare more general set-to-set binary
relations.

View original: http://arxiv.org/abs/1202.0425