{
  "id": "2203.02867",
  "version": "v1",
  "published": "2022-03-06T03:02:24.000Z",
  "updated": "2022-03-06T03:02:24.000Z",
  "title": "Diffusion Maps : Using the Semigroup Property for Parameter Tuning",
  "authors": [
    "Shan Shan",
    "Ingrid Daubechies"
  ],
  "comment": "14 pages, 12 figures",
  "categories": [
    "stat.ML",
    "cs.LG",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral parametrization for the manifold from simulated random walks or diffusion paths on the data set. However, DM is hard to tune in practice. In particular, the task to set a diffusion time t when constructing the diffusion kernel matrix is critical. We address this problem by using the semigroup property of the diffusion operator. We propose a semigroup criterion for picking t. Experiments show that this principled approach is effective and robust.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-06T03:02:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusion maps",
      "semigroup property",
      "parameter tuning",
      "classic dimension reduction technique",
      "diffusion kernel matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}