{
  "id": "1901.01341",
  "version": "v1",
  "published": "2019-01-04T23:44:47.000Z",
  "updated": "2019-01-04T23:44:47.000Z",
  "title": "Sheaves: A Topological Approach to Big Data",
  "authors": [
    "Linas Vepstas"
  ],
  "comment": "49 pages, 24 figures",
  "categories": [
    "cs.LG",
    "cs.DS",
    "cs.SC"
  ],
  "abstract": "This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that the data can be presented in terms of pair-wise relationships between objects/events. This assumption is used to mine for patterns in the dataset, defining a reduced graph or dataset that boils-down or concentrates information into a more compact form. The resulting extracted structure or set of patterns are manifestly symbolic in nature, as they capture and encode the graph structure of the dataset in terms of a (generative) grammar. This structure is identified as having the formal mathematical structure of a sheaf. In essence, this paper introduces the basic concepts of sheaf theory into the domain of graphical datasets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-04T23:44:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "big data",
      "topological approach",
      "pair-wise relationships",
      "assumption",
      "general concepts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}