  Topological data analysis (TDA) is an emerging technique for biological
signal processing. TDA leverages the invariant topological features of signals
in a metric space for robust analysis of signals even in the presence of noise.
In this paper, we leverage TDA on brain connectivity networks derived from
electroencephalogram (EEG) signals to identify statistical differences between
pediatric patients with obstructive sleep apnea (OSA) and pediatric patients
without OSA. We leverage a large corpus of data, and show that TDA enables us
to see a statistical difference between the brain dynamics of the two groups.
