A New Approximation Method of the Quadratic Discriminant Function

  • Shin’ichiro Omachi
  • Fang Sun
  • Hirotomo Aso
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)


For many statistical pattern recognition methods, distributions of sample vectors are assumed to be normal, and the quadratic discriminant function derived from the probability density function of multivariate normal distribution is used for classification. However, the computational cost is O(n 2) for n-dimensional vectors. Moreover, if there are not enough training sample patterns, covariance matrix can not be estimated accurately. In the case that the dimensionality is large, these disadvantages markedly reduce classification performance. In order to avoid these problems, in this paper, a new approximation method of the quadratic discriminant function is proposed. This approximation is done by replacing the values of small eigenvalues by a constant which is estimated by the maximum likelihood estimation. This approximation not only reduces the computational cost but also improves the classification accuracy.


Probability Density Function Training Sample Small Eigenvalue Multivariate Normal Distribution Minimum Description Length 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Shin’ichiro Omachi
    • 1
  • Fang Sun
    • 2
  • Hirotomo Aso
    • 1
  1. 1.Graduate School of EngineeringTohoku UniversitySendai-shiJapan
  2. 2.Faculty of Science and TechnologyTohoku Bunka Gakuen UniversitySendai-shiJapan

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