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International Conference on Neural Information Processing

ICONIP 2016: Neural Information Processing pp 224–232Cite as

A Corrector for the Sample Mahalanobis Distance Free from Estimating the Population Eigenvalues of Covariance Matrix

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9948))

Abstract

To correct the effect deteriorating the recognition performance of the sample Mahalanobis distance by a small number of learning sample, a new corrector for the sample Mahalanobis distance toward the corresponding population Mahalanobis distance is proposed without the population eigenvalues estimated from the sample covariance matrix defining the sample Mahalanobis distance. To omit computing the population eigenvalues difficult to estimate, the corrector uses the Stein’s estimator of covariance matrix. And the corrector also uses accurate expectation of the principal component of the sample Mahalanobis distance by the delta method in statistics. Numerical experiments show that the proposed corrector improves the probability distribution and the recognition performance in comparison with the sample Mahalanobis distance.

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References

  1. Ghasemi, E., Aaghaie, A., Cudney, E.A.: Mahalanobis Taguchi system: a review. Int. J. Qual. Reliab. Manag. 32(3), 291–307 (2015)

    Article  Google Scholar 

  2. Friedman, J.H.: Regularized discriminant analysis. J. Am. Statist. Assoc. 84(405), 165–175 (1989)

    Article  MathSciNet  Google Scholar 

  3. Kimura, F., Takashina, K., Tsuruoka, S., Miyake, Y.: Modified quadratic discriminant functions and the application to chinese character recognition. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9(1), 149–153 (1987)

    Article  Google Scholar 

  4. Sakai, M., Yoneda, M., Hase, H., Maruyama, H., Naoe, M.: A quadratic discriminant function based on bias rectification of eigenvalues. IEICE Trans. Inf. Syst. J82-D-II(4), 631–640 (1999). (in Japanese)

    Google Scholar 

  5. Iwamura, M., Omachi, S., Aso, H.: Estimation of true Mahalanobis distance from eigenvectors of sample covariance matrix. IEICE Trans. Inf. Syst. J86-D-II(1), 22–31 (2003). (in Japanese)

    MATH  Google Scholar 

  6. Kobayashi, Y.: A proposal of simple correcting scheme for sample Mahalanobis distances using delta method. IEICE Trans. Inf. Syst. J97-D(8), 1228–1236 (2014). (in Japanese)

    Google Scholar 

  7. James, W., Stein, C.: Estimation with quadratic loss. In: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 361–379 (1961)

    Google Scholar 

  8. Kobayashi, Y.: A simplified corrector for sample Mahalanobis distance. In: Proceedings of the 12th International Conference on Ubiquitous Healthcare, p. 109 (2015)

    Google Scholar 

  9. Oehlert, G.W.: A note on the delta method. Am. Statist. 46(1), 27–29 (1992)

    MathSciNet  Google Scholar 

  10. Lawley, D.N.: Tests of significance for the latent roots of covariance and correlation matrix. Biometrika 43, 128–136 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, New York (1990)

    MATH  Google Scholar 

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Acknowledgement

This research was partially supported by JSPS KAKENHI Grant Number JP15H02798.

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Authors and Affiliations

  1. Teikyo University, Faculty of Science and Engineering, Utsunomiya, Japan

    Yasuyuki Kobayashi

Authors
  1. Yasuyuki Kobayashi
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Corresponding author

Correspondence to Yasuyuki Kobayashi .

Editor information

Editors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Akira Hirose

  2. Kobe University, Kobe, Japan

    Seiichi Ozawa

  3. Okinawa Institute of Science and Technology Graduate University, Onna, Japan

    Kenji Doya

  4. Nara Institute of Science and Technology, Ikoma, Japan

    Kazushi Ikeda

  5. Kyungpook National University, Daegu, Korea (Republic of)

    Minho Lee

  6. Chinese Academy of Sciences, Beijing, China

    Derong Liu

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© 2016 Springer International Publishing AG

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Kobayashi, Y. (2016). A Corrector for the Sample Mahalanobis Distance Free from Estimating the Population Eigenvalues of Covariance Matrix. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9948. Springer, Cham. https://doi.org/10.1007/978-3-319-46672-9_26

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  • DOI: https://doi.org/10.1007/978-3-319-46672-9_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46671-2

  • Online ISBN: 978-3-319-46672-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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