  Graph topology inference, i.e., learning graphs from a given set of nodal
observations, is a significant task in many application domains. Existing
approaches are mostly limited to learning a single graph assuming that the
observed data is homogeneous. This is problematic because many modern datasets
are heterogeneous or mixed and involve multiple related graphs, i.e., multiview
graphs. Recent work proposing to learn multiview graphs ensures the similarity
of learned view graphs through pairwise regularization, where each pair of
views is encouraged to have similar structures. However, this approach cannot
infer the shared structure across views. In this work, we propose an
alternative method based on consensus regularization, where views are ensured
to be similar through a learned consensus graph representing the common
structure of the views. In particular, we propose an optimization problem,
where graph data is assumed to be smooth over the multiview graph and the
topology of the individual views and that of the consensus graph are learned,
simultaneously. Our optimization problem is designed to be general in the sense
that different regularization functions can be used depending on what the
shared structure across views is. Moreover, we propose two regularization
functions that extend fused and group graphical lasso to consensus based
regularization. Proposed multiview graph learning is evaluated on simulated
data and shown to have better performance than existing methods. It is also
employed to infer the functional brain connectivity networks of multiple
subjects from their electroencephalogram (EEG) recordings. The proposed method
reveals the structure shared by subjects as well as the characteristics unique
to each subject.
