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Signal classification with a point process distance on the space of persistence diagrams. (English) Zbl 1416.94030

Summary: 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.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
55N35 Other homology theories in algebraic topology

Software:

TDA; GitHub; Dionysus; Ripser
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References:

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