{
  "id": "1707.05926",
  "version": "v1",
  "published": "2017-07-19T03:12:35.000Z",
  "updated": "2017-07-19T03:12:35.000Z",
  "title": "Equivalence between LINE and Matrix Factorization",
  "authors": [
    "Qiao Wang",
    "Zheng Wang",
    "Xiaojun Ye"
  ],
  "comment": "5 pages",
  "categories": [
    "cs.LG"
  ],
  "abstract": "LINE [1], as an efficient network embedding method, has shown its effectiveness in dealing with large-scale undirected, directed, and/or weighted networks. Particularly, it proposes to preserve both the local structure (represented by First-order Proximity) and global structure (represented by Second-order Proximity) of the network. In this study, we prove that LINE with these two proximities (LINE(1st) and LINE(2nd)) are actually factoring two different matrices separately. Specifically, LINE(1st) is factoring a matrix M (1), whose entries are the doubled Pointwise Mutual Information (PMI) of vertex pairs in undirected networks, shifted by a constant. LINE(2nd) is factoring a matrix M (2), whose entries are the PMI of vertex and context pairs in directed networks, shifted by a constant. We hope this finding would provide a basis for further extensions and generalizations of LINE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-19T03:12:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "matrix factorization",
      "equivalence",
      "efficient network embedding method",
      "second-order proximity",
      "context pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}