{
  "id": "1404.3184",
  "version": "v1",
  "published": "2014-04-11T18:50:34.000Z",
  "updated": "2014-04-11T18:50:34.000Z",
  "title": "Decreasing Weighted Sorted $\\ell_1$ Regularization",
  "authors": [
    "Xiangrong Zeng",
    "Mário A. T. Figueiredo"
  ],
  "comment": "5 pages, 2 figures",
  "categories": [
    "cs.CV",
    "cs.IT",
    "cs.LG",
    "math.IT"
  ],
  "abstract": "We consider a new family of regularizers, termed {\\it weighted sorted $\\ell_1$ norms} (WSL1), which generalizes the recently introduced {\\it octagonal shrinkage and clustering algorithm for regression} (OSCAR) and also contains the $\\ell_1$ and $\\ell_{\\infty}$ norms as particular instances. We focus on a special case of the WSL1, the {\\sl decreasing WSL1} (DWSL1), where the elements of the argument vector are sorted in non-increasing order and the weights are also non-increasing. In this paper, after showing that the DWSL1 is indeed a norm, we derive two key tools for its use as a regularizer: the dual norm and the Moreau proximity operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-11T18:50:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decreasing",
      "regularization",
      "moreau proximity operator",
      "argument vector",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3184Z"
    }
  }
}