  Sparse inverse covariance estimation (i.e., edge de-tection) is an important
research problem in recent years, wherethe goal is to discover the direct
connections between a set ofnodes in a networked system based upon the observed
nodeactivities. Existing works mainly focus on unimodal distributions,where it
is usually assumed that the observed activities aregenerated from
asingleGaussian distribution (i.e., one graph).However, this assumption is too
strong for many real-worldapplications. In many real-world applications (e.g.,
brain net-works), the node activities usually exhibit much more complexpatterns
that are difficult to be captured by one single Gaussiandistribution. In this
work, we are inspired by Latent DirichletAllocation (LDA) [4] and consider
modeling the edge detectionproblem as estimating a mixture ofmultipleGaussian
distribu-tions, where each corresponds to a separate sub-network. Toaddress
this problem, we propose a novel model called GaussianMixture Graphical Lasso
(MGL). It learns the proportionsof signals generated by each mixture component
and theirparameters iteratively via an EM framework. To obtain
moreinterpretable networks, MGL imposes a special regularization,called Mutual
Exclusivity Regularization (MER), to minimize theoverlap between different
sub-networks. MER also addresses thecommon issues in read-world data sets,i.e.,
noisy observationsand small sample size. Through the extensive experiments
onsynthetic and real brain data sets, the results demonstrate thatMGL can
effectively discover multiple connectivity structuresfrom the observed node
activities
