{
  "id": "2310.13939",
  "version": "v1",
  "published": "2023-10-21T08:23:48.000Z",
  "updated": "2023-10-21T08:23:48.000Z",
  "title": "Asymptotic properties of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with their applications",
  "authors": [
    "Xiaoyu Liu",
    "Yiming Liu",
    "Guangming Pan",
    "Lingyue Zhang",
    "Zhixiang Zhang"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "This paper is to consider a general low-rank signal plus noise model in high dimensional settings. Specifically, we consider the noise with a general covariance structure and the signal to be at the same magnitude as the noise. Our study focuses on exploring various asymptotic properties related to the spiked eigenvalues and eigenvectors. As applications, we propose a new criterion to estimate the number of clusters, and investigate the properties of spectral clustering.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-21T08:23:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic properties",
      "spiked eigenvalues",
      "signal-plus-noise matrices",
      "eigenvectors",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}