Designing Classi ers for Fusion-Based Biometric Veri cation in .NET

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Designing Classi ers for Fusion-Based Biometric Veri cation
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Adaboost classifiers: Average Q values for the PIE database 1 0.9 0.8 Q value 0.7 0.6 0.5 0.4
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Authentic Q Impostor Q
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20 25 30 35 Threshold on PSR
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Figure 4.9. Average pairwise authentic and imposter Q values for the Adaboost ensemble on the
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impostor Q value of 1. Above a PSR threshold of 20, the individual authentic image decision is 1 for images of the same pose as the pose used in training the classi er and is 0 for most images of other poses. This would result in an authentic Q value close to 1 because most of the pairwise classi er decisions are different. There would be only a small variation between the second-order Q values of the 13 C2 different pairs of classi ers because of the symmetry between the pairs of classi ers. The average pairwise classi er authentic and impostor Q values over all persons are positive for the Adaboost ensemble as shown in Figure 4.9. The plot is obtained by rst averaging pairwise Q values for each person at a given threshold, and then averaging over all persons at that threshold. This averaging is different from that of other classi er ensembles because the number of classi ers in the Adaboost ensemble is person-dependent. The average pairwise classi er Q values are positive for the Bagging ensemble too, as seen in Figure 4.10. The positive Q values on both authentics and impostors are unfavorable for fusion. The performance curves for the OR rule ensemble and the best single classi er are Global ROCs. In other words, for a threshold on the match score (PSR), the proportion of authentic scores from all persons [which would be 15,210 (234 authentic scores per person *65 people) authentic scores] that are below this threshold would be an FRR point. The proportion of impostor scores from all persons [which would be 1,135,680 (17,472 impostor scores per person * 65 persons) impostor scores] that are above this thresholds would be the corresponding FAR point in this ROC. It should be noted that the ROC for the Adaboost is obtained differently. The Adaboost ROCs of each person are combined by averaging the FRRs of each persons
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4.4 Ensemble Design For Or rule Fusion
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Figure 4.10. Average pairwise authentic and imposter Q values of the Bagging ensemble on the
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ROC at a given FAR. This is done because the weights for the weighted decision fusion vary from person to person. Furthermore, there are different numbers of classi ers obtained by Adaboost for each person. The decision fusion ROCs for the Bagging ensemble are also averaged same as of Adaboost. This is because there is no correspondence between the classi ers of different persons. For a sample person, it is observed that the individual classi er EERs of the Adaboost ensemble are between 5% and 12%. The test set ROC of one UMACE lter per person, which is trained on all 39 authentic images, is displayed on Figure 4.11. The test set ROCs after fusion of proposed Or rule ensemble, the Adaboost and bagging ensembles are displayed in Figure 4.12. The equal error rate (EER) for the Or rule ensemble after Or fusion, the Adaboost ensemble after the corresponding weighted Majority fusion, the Bagging ensemble after Majority rule fusion and Or rule fusion, and the best single classi er are 0.75%, 6.2%, 9.3%, 4.7%, and 7.5%, respectively. It is important to note that the Or rule fusion is signi cantly better than Majority rule fusion for the Bagging ensemble. Majority fusion that is done in Bagging need not be the best fusion rule. The superiority of the proposed Or rule ensemble is proved here since its Or fusion accuracy is an order of magnitude more accurate than the others. The Or fusion is also the best decision fusion rule for the Or rule ensemble because their statistical dependence is optimal to the Or fusion rule. While the individual classi ers in the Adaboost and Bagging ensembles are superior to the individual classi ers of the Or rule ensemble, the positive pairwise classi er Q values are not favorable for fusion. Hence their fusion accuracy does not improve as signi cantly as observed for the Or rule ensemble.
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