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Empirical Risk Minimization for Variable Precision Dominance-Based Rough Set Approach

  • Yoshifumi Kusunoki
  • Jerzy Błaszczyński
  • Masahiro Inuiguchi
  • Roman Słowiński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8171)

Abstract

In this paper, we characterize Variable Precision Dominance-based Rough Set Approach (VP-DRSA) from the viewpoint of empirical risk minimization. VP-DRSA is an extension of the Dominance-based Rough Set Approach (DRSA) that admits some degree of misclassification error. From a definable set, we derive a classification function, which indicates assignment of an object to a decision class. Then, we define an empirical risk associated with the classification function. It is defined as mean hinge loss function. We prove that the classification function minimizing the empirical risk function corresponds to the lower approximation in VP-DRSA.

Keywords

rough sets variable precision dominance-based rough set approach empirical risk minimization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yoshifumi Kusunoki
    • 1
  • Jerzy Błaszczyński
    • 2
  • Masahiro Inuiguchi
    • 3
  • Roman Słowiński
    • 2
    • 4
  1. 1.Graduate School of EngineeringOsaka UniversitySuitaJapan
  2. 2.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  3. 3.Graduate School of Engineering ScienceOsaka UniversityToyonakaJapan
  4. 4.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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