EER of Fixed and Trainable Fusion Classifiers: A Theoretical Study with Application to Biometric Authentication Tasks

  • Norman Poh
  • Samy Bengio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3541)


Biometric authentication is a process of verifying an identity claim using a person’s behavioural and physiological characteristics. Due to the vulnerability of the system to environmental noise and variation caused by the user, fusion of several biometric-enabled systems is identified as a promising solution. In the literature, various fixed rules (e.g.min, max, median, mean ) and trainable classifiers (e.g. linear combination of scores or weighted sum) are used to combine the scores of several base-systems. How exactly do correlation and imbalance nature of base-system performance affect the fixed rules and trainable classifiers? We study these joint aspects using the commonly used error measurement in biometric authentication, namely Equal Error Rate (EER). Similar to several previous studies in the literature, the central assumption used here is that the class-dependent scores of a biometric system are approximately normally distributed. However, different from them, the novelty of this study is to make a direct link between the EER measure and the fusion schemes mentioned. Both synthetic and real experiments (with as many as 256 fusion experiments carried out on the XM2VTS benchmark score-level fusion data sets) verify our proposed theoretical modeling of EER of the two families of combination scheme. In particular, it is found that weighted sum can provide the best generalisation performance when its weights are estimated correctly. It also has the additional advantage that score normalisation prior to fusion is not needed, contrary to the rest of fixed fusion rules.


Equal Error Rate Biometric System False Acceptance Rate Biometric Authentication False Rejection Rate 
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  1. 1.
    Kuncheva, L.I.: A Theoretical Study on Six Classifier Fusion Strategies. IEEE Trans. Pattern Analysis and Machine Intelligence 24(2), 281–286 (2002)CrossRefGoogle Scholar
  2. 2.
    Tumer, K., Ghosh, J.: Robust Combining of Disparate Classifiers through Order Statistics. Pattern Analysis and Applications 5, 189–200 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fumera, G., Roli, F.: Analysis of Linear and Order Statistics Combiners for Fusion of Imbalanced Classifiers. In: Roli, F., Kittler, J. (eds.) MCS 2002. LNCS, vol. 2364, pp. 252–261. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Poh, N., Bengio, S.: How Do Correlation and Variance of Base Classifiers Affect Fusion in Biometric Authentication Tasks?, Research Report 04-18, IDIAP, Martigny, Switzerland (2004), accepted for publication in IEEE Trans. Signal Processing (2005)Google Scholar
  5. 5.
    Poh, N., Bengio, S.: Towards Predicting Optimal Subsets of Base-Experts in Biometric Authentication Task. IDIAP Research Report 04-17, Martigny, Switzerland, Accepted for publication in Joint AMI/PASCAL/IM2/M4 Workshop on Multimodal Interaction and Related Machine Learning Algorithms (2004)Google Scholar
  6. 6.
    Krogh, A., Vedelsby, J.: Neural Network Ensembles, Cross-Validation and Active-Learning. In: Advances in Neural Information Processing Systems vol. 7 (1995)Google Scholar
  7. 7.
    Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1999)Google Scholar
  8. 8.
    Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A First Course in Order Statistics. Wiley, New York (1992)zbMATHGoogle Scholar
  9. 9.
    Kittler, J., Hatef, M., Duin, R.P.W., Matas, J.: On Combining Classifiers. IEEE Trans. Pattern Analysis and Machine Intelligence 20(3), 226–239 (1998)CrossRefGoogle Scholar
  10. 10.
    Poh, N., Bengio, S.: “Database, Protocol and Tools for Evaluating Score-Level Fusion Algorithms in Biometric Authentication,” Research Report 04-44, IDIAP, Martigny, Switzerland (2005), Accepted for publication in AVBPA (2004)Google Scholar
  11. 11.
    Matas, J., Hamouz, M., Jonsson, K., Kittler, J., Li, Y., Kotropoulos, C., Tefas, A., Pitas, I., Tan, T., Yan, H., Smeraldi, F., Begun, J., Capdevielle, N., Gerstner, W., Ben-Yacoub, S., Abdeljaoued, Y., Mayoraz, E.: Comparison of Face Verification Results on the XM2VTS Database. In: Proc. 15th Int’l Conf. Pattern Recognition, Barcelona, vol. 4, pp. 858–863 (2000)Google Scholar
  12. 12.
    Bengio, S., Mariéthoz, J.: The Expected Performance Curve: a New Assessment Measure for Person Authentication. In: The Speaker and Language Recognition Workshop (Odyssey), Toledo, pp. 279–284 (2004)Google Scholar
  13. 13.
    Bengio, S., Mariéthoz, J.: A Statistical Significance Test for Person Authentication. In: The Speaker and Language Recognition Workshop (Odyssey), Toledo, pp. 237–244 (2004)Google Scholar
  14. 14.
    Jain, A., Nandakumar, K., Ross, A.: Score Normalisation in Multimodal Biometric Systems, In: Pattern Recognition (2005) (to appear)Google Scholar
  15. 15.
    Roli, F., Fumera, G., Kittler, J.: Fixed and Trained Combiners for Fusion of Imbalanced Pattern Classifiers. In: Proc. 5th Int’l Conf. on Information Fusion, pp. 278–284 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Norman Poh
    • 1
  • Samy Bengio
    • 1
  1. 1.IDIAP Research InstituteMartignySwitzerland

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