  Data-driven graph learning models a network by determining the strength of
connections between its nodes. The data refers to a graph signal which
associates a value with each graph node. Existing graph learning methods either
use simplified models for the graph signal, or they are prohibitively expensive
in terms of computational and memory requirements. This is particularly true
when the number of nodes is high or there are temporal changes in the network.
In order to consider richer models with a reasonable computational
tractability, we introduce a graph learning method based on representation
learning on graphs. Representation learning generates an embedding for each
graph node, taking the information from neighbouring nodes into account. Our
graph learning method further modifies the embeddings to compute the graph
similarity matrix. In this work, graph learning is used to examine brain
networks for brain state identification. We infer time-varying brain graphs
from an extensive dataset of intracranial electroencephalographic (iEEG)
signals from ten patients. We then apply the graphs as input to a classifier to
distinguish seizure vs. non-seizure brain states. Using the binary
classification metric of area under the receiver operating characteristic curve
(AUC), this approach yields an average of 9.13 percent improvement when
compared to two widely used brain network modeling methods.
