Nonparametric Discriminant Analysis Based on the Trace Ratio Criterion

  • Jin LiuEmail author
  • Qianqian Ge
  • Yanli Liu
  • Jing Dai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9242)


Feature extraction is a hot topic in machine learning and pattern recognition. This paper proposes a new nonparametric linear feature extraction method called nonparametric discriminant analysis based on the trace ratio criterion (TRNDA). The motivation comes principally from the nonparametric maximum margin criterion (NMMC). Based on nonparametric extensions of commonly used scatter matrices, an NMMC is one of the effective nonparametric methods of discriminant analysis for linear feature extraction. However, it is sensitive to outliers. By the proposed TRNDA, new scatter matrices are designed for reducing the influence of outliers, and the trace ratio algorithm is used to learn a set of orthogonal projections in succession. We evaluate the proposed method by several benchmark datasets and the results confirm its effectiveness.


Feature extraction Nonparametric discriminant analysis Trace ratio algorithm Orthogonal projections 



We would like to thank the associate editor and all anonymous reviewers for their constructive comments and suggestions. This research was partially supported by the National Science Foundation of China (Grant No. 61101246) and the Fundamental Research Funds for the Central Universities (Grant No. JB150209).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Electronic EngineeringXidian UniversityXi’anChina
  2. 2.School of Electromechanical and InformationHebei United University, Qian’an CollegeTangshanChina

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