{
  "id": "1506.02633",
  "version": "v1",
  "published": "2015-06-08T19:39:37.000Z",
  "updated": "2015-06-08T19:39:37.000Z",
  "title": "A Topological Approach to Spectral Clustering",
  "authors": [
    "Antonio Rieser"
  ],
  "comment": "9 Pages",
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "We propose a clustering algorithm which, for input, takes data assumed to be sampled from a uniform distribution supported on a metric space $X$, and outputs a clustering of the data based on a topological estimate of the connected components of $X$. The algorithm works by choosing a weighted graph on the samples from a natural one-parameter family of graphs using an error based on the heat operator on the graphs. The estimated connected components of $X$ are identified as the support of the eigenfunctions of the heat operator with eigenvalue $1$, which allows the algorithm to work without requiring the number of expected clusters as input.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-08T19:39:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological approach",
      "spectral clustering",
      "heat operator",
      "connected components",
      "uniform distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}