{
  "id": "1305.3879",
  "version": "v3",
  "published": "2013-05-16T18:01:32.000Z",
  "updated": "2014-02-20T17:24:17.000Z",
  "title": "Persistent Homology of Delay Embeddings",
  "authors": [
    "Saba Emrani",
    "Thanos Gentimis",
    "Hamid Krim"
  ],
  "comment": "16 pages, 8 figures",
  "categories": [
    "math.AT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-02-20T17:24:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N35",
      "55N99",
      "55U99"
    ],
    "keywords": [
      "persistent homology",
      "delay embeddings",
      "delay-coordinate embeddings",
      "first betti numbers",
      "periodic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.3879E"
    }
  }
}