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Empirical risk minimization and problems of constructing linear classifiers

  • Y. P. Laptin
  • Y. I. Zhuravlev
  • A. P. Vinogradov
Article
  • 43 Downloads

Abstract

Problems of construction of linear classifiers for classifying many sets are considered. In the case of linearly separable sets, problem statements are given that generalize already well-known formulations. For linearly inseparable sets, a natural criterion for choosing a classifier is empirical risk minimization. A mixed integer formulation of the empirical risk minimization problem and possible solutions of its continuous relaxation are considered. The proposed continuous relaxation problem is compared with problems solved with the help of other approaches to the construction of linear classifiers. Features of nonsmooth optimization methods used to solve the formulated problems are described.

Keywords

linear classification algorithm linear separability of sets empirical risk support vector method optimization method 

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • Y. P. Laptin
    • 1
  • Y. I. Zhuravlev
    • 2
  • A. P. Vinogradov
    • 2
  1. 1.V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of UkraineKyivUkraine
  2. 2.A. A. Dorodnitsyn Computing CenterRussian Academy of SciencesMoscowRussia

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