In this paper, we consider the problem of signal classification. First, the signal is translated into a persistence diagram through the use of delay-embedding and persistent homology. Endowing the data space of persistence diagrams with a metric from point processes, we show that it admits statistical structure in the form of Fréchet means and variances and a classification scheme is established. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and changes in cardinality. The classification results using this distance are benchmarked on both synthetic data and real acoustic signals and it is demonstrated that this classifier outperforms current signal classification techniques.
Marchese, A., & Maroulas, V. (2018). Signal classification with a point process distance on the space of persistence diagrams. Advances in Data Analysis and Classification, 12(3), 657–682. https://doi.org/10.1007/s11634-017-0294-x