{
  "id": "0805.4220",
  "version": "v1",
  "published": "2008-05-27T21:15:22.000Z",
  "updated": "2008-05-27T21:15:22.000Z",
  "title": "Best subspace tensor approximations",
  "authors": [
    "S. Friedland",
    "V. Mehrmann"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NA",
    "math.OC"
  ],
  "abstract": "In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained via the singular value decomposition which allows to compute the best rank $k$ approximations. For $t$-tensors with $t>2$ many generalizations of the singular value decomposition have been proposed to obtain low tensor rank decompositions. In this paper we will present a different approach which is based on best subspace approximations, which present an alternative generalization of the singular value decomposition to tensors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-27T21:15:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "15A69",
      "65D15",
      "65H10",
      "65K05"
    ],
    "keywords": [
      "best subspace tensor approximations",
      "singular value decomposition",
      "low tensor rank decompositions",
      "best subspace approximations",
      "genomic data analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.4220F"
    }
  }
}