Monday, April 3, 2017 - 12:00pm to 1:15pm
University of Tennessee
Persistence diagrams classification using a point process distance: an application to signals
In this talk, we consider the problem of signal classification by considering their associated persistence diagrams. We endow the data space of persistence diagrams with a new metric from point processes. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and changes in cardinality. Pulling back to the space of signals, this corresponds to detecting differences in a signal’s periodicity, underlying noise, and geometry. The metric space of persistence diagrams is proved to admit statistical structure in the form of Fréchet means and variances. The new classification method using this distance is benchmarked on both synthetic data and real acoustic signals. Bio: Vasileios Maroulas is an Associate Professor of Mathematics and Business Analytics and Statistics at the University of Tennessee. His research interests span from computational statistics to applied probability and computational topology and geometry with applications in data analysis. He received the PhD in Statistics from the University of North Carolina at Chapel Hill in 2008, and subsequently he was a Lockheed Martin Postdoctoral Fellow at the IMA at the University of Minnesota. He joined as an Assistant Professor the University of Tennessee in 2010, and he was a Leverhulme Trust Fellow at the University of Bath, UK during 2013-2014.