{
  "id": "1902.03840",
  "version": "v1",
  "published": "2019-02-11T12:14:36.000Z",
  "updated": "2019-02-11T12:14:36.000Z",
  "title": "On the rotational invariant $L_1$-norm PCA",
  "authors": [
    "Sebastian Neumayer",
    "Max Nimmer",
    "Simon Setzer",
    "Gabriele Steidl"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "Principal component analysis (PCA) is a powerful tool for dimensionality reduction. Unfortunately, it is sensitive to outliers, so that various robust PCA variants were proposed in the literature. Among them the so-called rotational invariant $L_1$-norm PCA is rather popular. In this paper, we reinterpret this robust method as conditional gradient algorithm and show moreover that it coincides with a gradient descent algorithm on Grassmannian manifolds. Based on this point of view, we prove for the first time convergence of the whole series of iterates to a critical point using the Kurdyka-{\\L}ojasiewicz property of the energy functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-11T12:14:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rotational invariant",
      "norm pca",
      "principal component analysis",
      "robust pca variants",
      "conditional gradient algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}