{
  "id": "1601.04364",
  "version": "v1",
  "published": "2016-01-17T23:30:47.000Z",
  "updated": "2016-01-17T23:30:47.000Z",
  "title": "Spectral identification of networks using sparse measurements",
  "authors": [
    "A. Mauroy",
    "J. Hendrickx"
  ],
  "comment": "35",
  "categories": [
    "math.DS",
    "cs.SY"
  ],
  "abstract": "We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph topology, we focus on the identification of the spectral graph-theoretic properties of the network, a framework that we call spectral network identification. The main theoretical results connect the spectral properties of the network to the spectral properties of the dynamics, which are well-defined in the context of the so-called Koopman operator and can be extracted from data through the Dynamic Mode Decomposition algorithm. These results are obtained for networks of diffusively-coupled units that admit a stable equilibrium state. For large networks, a statistical approach is considered, which focuses on spectral moments of the network and is well-suited to the case of heterogeneous populations. Our framework provides efficient numerical methods to infer global information on the network from sparse local measurements at a few nodes. Numerical simulations show for instance the possibility of detecting the mean number of connections or the addition of a new vertex using measurements made at one single node, that need not be representative of the other nodes' properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-17T23:30:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sparse measurements",
      "spectral identification",
      "spectral properties",
      "dynamic mode decomposition algorithm",
      "full graph topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160104364M"
    }
  }
}