Persistent Homology of Delay Embeddings

Saba Emrani; Thanos Gentimis; Hamid Krim

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arXiv · 1305.3879

Persistent Homology of Delay Embeddings

Saba Emrani·Thanos Gentimis·Hamid Krim

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Abstract

The objective of this study is to detect and quantify the periodic behavior of the signals using topological methods. We propose to use delay-coordinate embeddings as a tool to measure the periodicity of signals. Moreover, we use persistent homology for analyzing the structure of point clouds of delay-coordinate embeddings. A method for finding the appropriate value of delay is proposed based on the autocorrelation function of the signals. We apply this topological approach to wheeze signals by introducing a model based on their harmonic characteristics. Wheeze detection is performed using the first Betti numbers of a few number of landmarks chosen from embeddings of the signals.

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BibTeX RIS

Saba Emrani, Thanos Gentimis, Hamid Krim. 2013-05-16. Persistent Homology of Delay Embeddings. https://arxiv.org/abs/1305.3879

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