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Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 81))

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Abstract

Various statistically-based classification methods use entropy functions for error bounds evaluation and feature selection. A lot of such entropy functions are known, each of them providing a measure of “distance” between probability distributions. But in practice, these probability distributions are never precisely known, they are estimated by means of the training set.

In this paper, we introduce one concept of entropy measure e, which is not related to probabilities; e is directly expressed in terms of frequencies, in such a way that e is sensitive to the sample size.

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References

  1. Arimoto, S. Information Theoretical Considerations and Estimation Problems. Information and Control 19, 181, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, C.H. On the Use of Distance and Information Measures in Pattern Recognition and Applications. Pattern Recognition Theory and Application, NATO Advanced Study Inst. Series, K.S. Fu and A.B. Whinston ed. 45, 1977.

    Google Scholar 

  3. Daroczy, Z. Generalised Information Functions. Information and Control 16, 36, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  4. Devijver, P. On Information Measure in Identification and Parameter Estimation. Proc. 3rd IFAC Symp. Identification and System Parameter Estimation, 631, 1973.

    Google Scholar 

  5. Devijver, P. Entropies of Degree 3 and Lower Bounds for the Average Error Rate. Information and Control 34, 222, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  6. Gaillat, G. Une Procedure Statistique de Decision avec Apprentissage et son Application a la Reconnaissance de Caracteres Manuscrits. These 3eme cycle, Paris V I, 1975.

    Google Scholar 

  7. Terrenoire, M. Tounissoux, D. Consideration of the Data Uncertainty with Regard to the Sequential Decision Scheme. Pattern Recognition Theory and Applications NATO Advanced Study Inst. Series., K.S. Fu and A.B. Whinston ed, 91, 1977.

    Google Scholar 

  8. Terrenoire M, Tounissoux D. Une Technique de Reconnaissance de Forme pour des Ensembles d’Apprentissage de Petite Taille. Seminaire IRIA. Classification automatique et perception par ordinateur, 113, 1979.

    Google Scholar 

  9. Tounissoux, D. Processus Sequentiel s Adaptatifs de Reconnaissance de Formes pour l’Aide au Diagnostic. These, Lyon, 1980.

    Google Scholar 

  10. Vajda, I. Bounds of the Minimal Error Probability on Checking a Finite or Countable Number of Hypotheses. Problemy Peredachi Informatsii, Vol. 4, No. 1, 9, 1968.

    MathSciNet  Google Scholar 

  11. Vajda I. Limit Theorems for Total Variation of Cartesian Product Measures. Studia Scientiarum Mathematicarum Hungarica, 6, 317, 1971.

    MathSciNet  Google Scholar 

  12. Van Tree. Decision, Estimation and Modulation Theory. Wiley, 1968.

    Google Scholar 

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© 1982 D. Reidel Publishing Company

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Terrenoire, M., Tounissoux, D. (1982). Sample Size Sensitive Entropy. In: Kittler, J., Fu, K.S., Pau, LF. (eds) Pattern Recognition Theory and Applications. NATO Advanced Study Institutes Series, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7772-3_5

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  • DOI: https://doi.org/10.1007/978-94-009-7772-3_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7774-7

  • Online ISBN: 978-94-009-7772-3

  • eBook Packages: Springer Book Archive

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