Persistent topology of decision boundaries

Topological signal processing, especially persistent homology, is a growing field of study for analyzing sets of data points that has been heretofore applied to unlabeled data. In this work, we consider the case of labeled data and examine the topology of the decision boundary separating different labeled classes. Specifically, we propose a novel approach to construct simplicial complexes of decision boundaries, which can be used to understand their topology. Furthermore, we illustrate one use case for this line of theoretical work in kernel selection for supervised classification problems.