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Classification on the Data Space of Persistence Diagrams

Dr. Vasileios Maroulas
Professor of Mathematics
University of Tennessee
November 3, 2017   2:30-3:30pm
JDT 410

Abstract: Two years ago, the US Army Research Lab contacted me and requested if I could help to classify acoustic signals by developing a different method from the current state of art.  Indeed, 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, which 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. Two years fast forward, the new classification method using this distance is successfully benchmarked on both synthetic data and the US acoustic yielding new insights in signal classification.

Bio: Vasileios Maroulas is an Associate Professor of Mathematics 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. His research has been funded by numerous agencies, and has strong connections with the industry involving data science. He received a 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. He also received the Excellence in Research and Creative Achievement Award by the College of Arts and Sciences at UTK.