{
  "id": "1703.06700",
  "version": "v1",
  "published": "2017-03-20T12:09:53.000Z",
  "updated": "2017-03-20T12:09:53.000Z",
  "title": "Independence clustering (without a matrix)",
  "authors": [
    "Daniil Ryabko"
  ],
  "categories": [
    "cs.LG",
    "cs.IT",
    "math.IT",
    "stat.ML"
  ],
  "abstract": "The independence clustering problem is considered in the following formulation: given a set $S$ of random variables, it is required to find the finest partitioning $\\{U_1,\\dots,U_k\\}$ of $S$ into clusters such that the clusters $U_1,\\dots,U_k$ are mutually independent. Since mutual independence is the target, pairwise similarity measurements are of no use, and thus traditional clustering algorithms are inapplicable. The distribution of the random variables in $S$ is, in general, unknown, but a sample is available. Thus, the problem is cast in terms of time series. Two forms of sampling are considered: i.i.d.\\ and stationary time series, with the main emphasis being on the latter, more general, case. A consistent, computationally tractable algorithm for each of the settings is proposed, and a number of open directions for further research are outlined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-20T12:09:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random variables",
      "stationary time series",
      "mutual independence",
      "pairwise similarity measurements",
      "independence clustering problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}