{
  "id": "2005.12263",
  "version": "v1",
  "published": "2020-05-23T04:28:45.000Z",
  "updated": "2020-05-23T04:28:45.000Z",
  "title": "Principal Component Analysis Based on T$\\ell_1$-norm Maximization",
  "authors": [
    "Xiang-Fei Yang",
    "Yuan-Hai Shao",
    "Chun-Na Li",
    "Li-Ming Liu",
    "Nai-Yang Deng"
  ],
  "categories": [
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "Classical principal component analysis (PCA) may suffer from the sensitivity to outliers and noise. Therefore PCA based on $\\ell_1$-norm and $\\ell_p$-norm ($0 < p < 1$) have been studied. Among them, the ones based on $\\ell_p$-norm seem to be most interesting from the robustness point of view. However, their numerical performance is not satisfactory. Note that, although T$\\ell_1$-norm is similar to $\\ell_p$-norm ($0 < p < 1$) in some sense, it has the stronger suppression effect to outliers and better continuity. So PCA based on T$\\ell_1$-norm is proposed in this paper. Our numerical experiments have shown that its performance is superior than PCA-$\\ell_p$ and $\\ell_p$SPCA as well as PCA, PCA-$\\ell_1$ obviously.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-23T04:28:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "norm maximization",
      "stronger suppression effect",
      "classical principal component analysis",
      "robustness point",
      "better continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}