{
  "id": "1106.4075",
  "version": "v1",
  "published": "2011-06-21T02:49:12.000Z",
  "updated": "2011-06-21T02:49:12.000Z",
  "title": "On the Inclusion Relation of Reproducing Kernel Hilbert Spaces",
  "authors": [
    "Haizhang Zhang",
    "Liang Zhao"
  ],
  "categories": [
    "math.FA",
    "cs.LG"
  ],
  "abstract": "To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-21T02:49:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reproducing kernel hilbert spaces",
      "inclusion relation",
      "widely-used translation invariant kernels",
      "feature maps",
      "norm equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.4075Z"
    }
  }
}