Caprice 3-4
Analysis of Signal Classification via Persistent Homology (304788)
*Cassie Putman Micucci, University of TennesseeVasileios Maroulas, University of Tennessee
Keywords: Classification of Time Series, Data Space of Persistence Diagrams, Wasserstein Metric, Cardinality, Persistent homology
Classification of signals is a well-known problem within machine learning, although many methods overlook significant geometric or topological structure in the data. To investigate these features, we create a persistence diagram after transforming a signal into a point cloud using Takens’ embedding. We then consider a new metric on the space of persistence diagrams that accounts both for the matching of points and for the cardinality of the diagrams. This metric generates a classification algorithm for the signals. We also investigate the stability properties of this metric; this analysis provides justification for the use of the metric for comparisons of such diagrams.