{
  "id": "2304.03727",
  "version": "v1",
  "published": "2023-04-07T16:45:53.000Z",
  "updated": "2023-04-07T16:45:53.000Z",
  "title": "Equilibrium Distributions for t-distributed Stochastic Neighbour Embedding",
  "authors": [
    "Antonio Auffinger",
    "Daniel Fletcher"
  ],
  "comment": "28 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the empirical measure of the output of the t-distributed stochastic neighbour embedding algorithm when the initial data is given by n independent, identically distributed inputs. We prove that under certain assumptions on the distribution of the inputs, this sequence of measures converges to an equilibrium distribution, which is described as a solution of a variational problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-07T16:45:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equilibrium distribution",
      "t-distributed stochastic neighbour embedding algorithm",
      "measures converges",
      "variational problem",
      "initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}