  Graph signal processing (GSP) is a key tool for satisfying the growing demand
for information processing over networks. However, the success of GSP in
downstream learning and inference tasks is heavily dependent on the prior
identification of the relational structures. Graphs are natural descriptors of
the relationships between entities of complex environments. The underlying
graph is not readily detectable in many cases and one has to infer the topology
from the observed signals. Firstly, we address the problem of graph signal
classification by proposing a novel framework for discriminative graph
learning. To learn discriminative graphs, we invoke the assumption that signals
belonging to each class are smooth with respect to the corresponding graph
while maintaining non-smoothness with respect to the graphs corresponding to
other classes. Secondly, we extend our work to tackle increasingly dynamic
environments and real-time topology inference. We develop a proximal gradient
(PG) method which can be adapted to situations where the data are acquired
on-the-fly. Beyond discrimination, this is the first work that addresses the
problem of dynamic graph learning from smooth signals where the sought network
alters slowly. The validation of the proposed frameworks is comprehensively
investigated using both synthetic and real data.
