Applying the Upper Integral to the Biometric Score Fusion Problem in the Identification Model
Abstract
:1. Introduction
2. Fuzzy Measure and Upper Integral
2.1. Fuzzy Measure
- (1)
- Boundary conditions: , .
- (2)
- Monotonicity: if and .
- (3)
- Continuity: if and are monotone (an increasing sequence of measurable sets).
2.2. Upper Integral
3. Proposed Method
3.1. The Fusion Model Based on the Upper Integral
3.2. Determining Fuzzy Densities
4. Experimental Results
5. Conclusions
Author Contributions
Conflicts of Interest
References
- Jain, A.K.; Flynn, P.; Ross, A. Handbook of Biometrics; Springer: Berlin, Germany, 2008. [Google Scholar]
- Jain, A.K.; Ross, A.; Prabhakar, S. An introduction to biometric recognition. IEEE Trans. Circuits Syst. Video Technol. 2004, 14, 4–20. [Google Scholar] [CrossRef]
- Nandakumar, K.; Jain, A.K.; Ross, A. Fusion in Multibiometric Identification Systems: What about the Missing Data? In Advances in Biometrics, Proceedings of the Third International Conference, ICB 2009, Alghero, Italy, 2–5 June 2009; Tistarelli, M., Nixon, M.S., Eds.; Lecture Notes in Computer Science. Springer: Berlin/Heidelberg, Germany, 2009; Volume 5558, pp. 743–752. [Google Scholar]
- Jain, A.K.; Nandakumar, K.; Ross, A. Score normalization in multimodal biometric systems. Pattern Recognit. 2005, 38, 2270–2285. [Google Scholar] [CrossRef]
- Ross, A.; Nandakumar, K.; Jain, A.K. Handbook of Multibiometrics; Springer: Secaucus, NJ, USA, 2006. [Google Scholar]
- Nandakumar, K.; Chen, Y.; Dass, S.C.; Jain, A.K. Likelihood Ratio Based Biometric Score Fusion. IEEE Trans. Pattern Anal. Mach. Intell. 2008, 2, 342–347. [Google Scholar] [CrossRef] [PubMed]
- Liau, H.F.; Isa, D. Feature selection for support vector machine-based face-iris multimodal biometric system. Expert Syst. Appl. 2011, 38, 11105–11111. [Google Scholar] [CrossRef]
- Tulyakov, S.; Chaohong, W.; Govindaraju, V. Iterative Methods for Searching Optimal Classifier Combination Function. In Proceedings of the 2007 First IEEE International Conference on Biometrics: Theory, Applications, and Systems, Crystal City, VA, USA, 27–29 September 2007; pp. 1–5.
- Yishu, L.; Lihua, Y.; Suen, C.Y. The Effect of Correlation and Performances of Base-Experts on Score Fusion. IEEE Transac. Syst. Man Cybern. Syst. 2014, 44, 510–517. [Google Scholar]
- Daugman, J. Biometric Decision Landscapes; Tech. Rep. TR482; Computer Laboratory, University of Cambridge: Cambridge, MA, USA, 2000. [Google Scholar]
- Vatsa, M.; Singh, R.; Noore, A.; Houck, M. Quality-augmented fusion of level-2 and level-3 fingerprint information using DSm theory. Int. J. Approx. Reason. 2009, 50, 51–61. [Google Scholar] [CrossRef]
- Zadeh, L.A. Fuzzy sets. Inf. Control 1965, 3, 338–353. [Google Scholar] [CrossRef]
- Temkoa, A.; Machob, D.; Nadeua, C. Fuzzy integral based information fusion for classification of highly confusable non-speech sounds. Pattern Recognit. 2008, 41, 1814–1823. [Google Scholar] [CrossRef]
- Pham, T.; Wagner, M. Similarity normalization for speaker verification by fuzzy fusion. Pattern Recognit. 2000, 33, 309–315. [Google Scholar] [CrossRef]
- Kwak, K.-C.; Pedrycz, W. Face recognition: A study in information fusion using fuzzy integral. Pattern Recognit. Lett. 2005, 26, 719–733. [Google Scholar] [CrossRef]
- Khalifa, A.B.; Gazzah, S.; BenAmara, N.E. Multimodal Biometric Authentication Using Choquet Integral and Genetic Algorithm. Int. J. Comput. Inf. Sci. Eng. 2013, 7, 976–986. [Google Scholar]
- Murofushi, T.; Sugeno, M.; Machida, M. Non-monotonic fuzzy measures and the Choquet integral. Fuzzy Sets Syst. 1994, 64, 73–86. [Google Scholar] [CrossRef]
- Sugeno, M. Theory of Fuzzy Integral and Its Applications. Ph.D. Thesis, Tokyo Institute of Technology, Tokyo, Japan, 1974. [Google Scholar]
- Wang, Z.; Li, W.; Leung, K.-S. Lower integrals and upper integrals with respect to nonadditive set functions. Fuzzy Sets Syst. 2008, 159, 646–660. [Google Scholar] [CrossRef]
- Chen, A.-X.; Liang, Z.-Y.; Feng, H.-M. Classification based on upper integral. In Proceedings of the 2011 International Conference on Machine Learning and Cybernetics (ICMLC), Guilin, China, 10–13 July 2011; pp. 835–840.
- Wang, X.-Z.; Wang, R.; Feng, H.-M.; Wang, H.-C. A New Approach to Classifier Fusion Based on Upper Integral. IEEE Transac. Cybern. 2014, 44, 620–635. [Google Scholar] [CrossRef] [PubMed]
- Feng, H.-M.; Wang, X.-Z. Performance improvement of classifier fusion for batch samples based on upper integral. Neural Netw. 2015, 63, 87–93. [Google Scholar] [CrossRef] [PubMed]
- Fakhar, K.; El Aroussi, M.; Saidi, M.N.; Aboutajdine, D. Score Fusion in Multibiometric Identification Based on Fuzzy Set Theory. In Image and Signal Processing; Elmoataz, A., Mammass, D., Lezoray, O., Nouboud, F., Aboutajdine, D., Eds.; Springer: Heidelberg, Germany, 2012; Volume 7340, pp. 261–268. [Google Scholar]
- Sugeno, M. Fuzzy measures and fuzzzy integrals: A survey. Fuzzy Autom. Decis. Process. 1977. [Google Scholar] [CrossRef]
- Wang, Z.; Leung, K.-S.; Wong, M.-L.; Fang, J. A new type of nonlinear integrals and the computational algorithm. Fuzzy Sets Syst. 2000, 112, 223–231. [Google Scholar] [CrossRef]
- De Luca, A.; Termini, S. A definition of a nonprobalistic entropy in the setting of fuzzy entropy. Inform. Control 1972, 20, 301–312. [Google Scholar] [CrossRef]
- Wang, Z.; Leung, K.-S.; Wang, J. A genetic algorithm for determining nonadditive set functions in information fusion. Fuzzy Sets Syst. 1999, 102, 463–469. [Google Scholar] [CrossRef]
- Pham, T.D.; Hong, Y. Information fusion by fuzzy integral. In Proceedings of the 1996 Australian and New Zealand Conference on Intelligent Information Systems, Adelaide, Australia, 18–20 November 1996; pp. 191–194.
- Liu, Y.; Li, X.; Zhuang, Z. Decision-level Information Fusion for Target Recognition Based on Choquet Fuzzy Integral. J. Electron. Inf. Technol. 2003, 25, 695–699. [Google Scholar]
- Murofushi, T.; Sugeno, M. An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets Syst. 1989, 29, 201–227. [Google Scholar] [CrossRef]
- Gader, P.D.; Mohamed, M.A.; Keller, J.M. Fusion of handwritten word classifiers. Pattern Recognit. Lett. 1996, 17, 577–584. [Google Scholar] [CrossRef]
- Wang, X.-Z.; Wang, X.-J. A new methodology for determining fuzzy densities in the fusion model based on fuzzy integral. In Proceedings of the 2004 International Conference on Machine Learning and Cybernetics, Shanghai, China, 26–29 August 2004; Volume 4, pp. 2028–2031.
- National Institute of Standards and Technology: NIST Biometric Scores Set, 2004. Available online: http://www.nist.gov/itl/iad/ig/biometricscores.cfm (accessed on 9 June 2015).
© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Fakhar, K.; Aroussi, M.E.; Saidi, M.N.; Aboutajdine, D. Applying the Upper Integral to the Biometric Score Fusion Problem in the Identification Model. Information 2015, 6, 494-504. https://doi.org/10.3390/info6030494
Fakhar K, Aroussi ME, Saidi MN, Aboutajdine D. Applying the Upper Integral to the Biometric Score Fusion Problem in the Identification Model. Information. 2015; 6(3):494-504. https://doi.org/10.3390/info6030494
Chicago/Turabian StyleFakhar, Khalid, Mohamed El Aroussi, Mohamed Nabil Saidi, and Driss Aboutajdine. 2015. "Applying the Upper Integral to the Biometric Score Fusion Problem in the Identification Model" Information 6, no. 3: 494-504. https://doi.org/10.3390/info6030494
APA StyleFakhar, K., Aroussi, M. E., Saidi, M. N., & Aboutajdine, D. (2015). Applying the Upper Integral to the Biometric Score Fusion Problem in the Identification Model. Information, 6(3), 494-504. https://doi.org/10.3390/info6030494