Classification on the space of persistence diagrams

Le candidat pour le poste de professeur en statistique, Vasileios Maroulas, présentera une conférence le jeudi 14 décembre à 10:30 dans la salle 6214.

Voici le sujet de sa conférence : Classification on the space of persistence diagrams

In this talk, we consider the problem of time series classification by considering their associated persistence diagrams. We endow the data space of persistence diagrams with a new metric. 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.