  Sleep apnea is a disorder that has serious consequences for the pediatric
population. There has been recent concern that traditional diagnosis of the
disorder using the apnea-hypopnea index may be ineffective in capturing its
multi-faceted outcomes. In this work, we take a first step in addressing this
issue by phenotyping patients using a clustering analysis of airflow time
series. This is approached in three ways: using feature-based fuzzy clustering
in the time and frequency domains, and using persistent homology to study the
signal from a topological perspective. The fuzzy clusters are analyzed in a
novel manner using a Dirichlet regression analysis, while the topological
approach leverages Takens embedding theorem to study the periodicity properties
of the signals.
