{
  "id": "1612.02513",
  "version": "v1",
  "published": "2016-12-08T02:42:20.000Z",
  "updated": "2016-12-08T02:42:20.000Z",
  "title": "Complex Matrix Factorization for Face Recognition",
  "authors": [
    "Viet-Hang Duong",
    "Yuan-Shan Lee",
    "Bach-Tung Pham",
    "Seksan Mathulaprangsan",
    "Pham The Bao",
    "Jia-Ching Wang"
  ],
  "comment": "4 pages,3 figures,4 tables",
  "categories": [
    "cs.CV"
  ],
  "abstract": "This work developed novel complex matrix factorization methods for face recognition; the methods were complex matrix factorization (CMF), sparse complex matrix factorization (SpaCMF), and graph complex matrix factorization (GraCMF). After real-valued data are transformed into a complex field, the complex-valued matrix will be decomposed into two matrices of bases and coefficients, which are derived from solutions to an optimization problem in a complex domain. The generated objective function is the real-valued function of the reconstruction error, which produces a parametric description. Factorizing the matrix of complex entries directly transformed the constrained optimization problem into an unconstrained optimization problem. Additionally, a complex vector space with N dimensions can be regarded as a 2N-dimensional real vector space. Accordingly, all real analytic properties can be exploited in the complex field. The ability to exploit these important characteristics motivated the development herein of a simpler framework that can provide better recognition results. The effectiveness of this framework will be clearly elucidated in later sections in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-08T02:42:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "face recognition",
      "optimization problem",
      "novel complex matrix factorization methods",
      "work developed novel complex matrix",
      "2n-dimensional real vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}