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sum 78 180 75 135 83 88 68 166 61 161 89 1-comiss identified 67 1 92 1 92 1 9 93 1 92 1 6 88 1 2 96 1 93 1 82 1 47 0 49 55 1 total correct 958 % false pos total avail 1184 66 9 % correct 74 81 1 % false neg 0
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1-comiss identified 73 1 83 1 98 1 .18 80 1 89 1 .05 94 1 .03 96 1 89 1 88 1 92 1 .73 74 1 total correct 10 % false pos .99 total avail 11 0 % correct 74 87 1 % false neg 0
Figure 17.18. (a) Sample contingency matrix. (b) Normalized contingency matrix. The 11 extracted subjects illustrate the conversion between classi cation of heartbeats and identi cation of individuals. Based on voting, the marginal statistics show the classi cation of subjects. A 1 in the identi ed row indicates that the correct subject was identi ed.
17.4 Implementation and Performance
column occurs along the major diagonal, then the subject is correctly identi ed that is, voting. Errors occurring along the column are errors of omission. For a veri cation system, these are false-negative errors where an authorized user cannot gain access. Errors along the row are errors of commission. Commission errors are false acceptance errors, where an unauthorized user (intruder) gains access to the system. The identi cation error rates cited here are the average of the omission and commission values. Figure 17.18a highlights a number of interpretation issues. First, the contingency matrix is not symmetrical. So, the rate of false acceptance between individuals is not the same. The number of heartbeats acquired is not the same for all individuals. The variable number of examples percolates through the contingency matrix. For Subject B, approximately 30% of the heartbeats have a commission error with Subject J. These heartbeats are over 50% of the total assigned to Subject J. If the two subjects contained the same number of heartbeats, then no confusion or false acceptance of Subject B to Subject J would occur. A normalization procedure, called iterative proportional tting [45], could be applied if it were assumed that the number of heartbeats from all individuals is the same (Figure 17.18b). For these experiments, no assumptions about the relative likelihoods for assigning heartbeats were made.
ECG Identi cation
From the original 15 attributes, 9 attributes were commonly selected during the majority of experimental constraints of canonical relationships. A stepwise canonical correlation that used the Wilkes lambda as a divergence measure provided the feature selection [46]. The feature selection process was performed to ensure stable discrimination. The nine commonly used attributes were: RQ, RS, RP , RT, Twidth, ST, PQ, LQ, and T L (interbeat interval), Figure 17.10. To use ECG as a biometric, individuals will enroll their information into the security system. After enrollment, the user s ECG will be interrogated by the system. Unlike the traditional static biometrics, heartbeat signals vary with stress. The state of anxiety and the relative orientation of the ECG electrodes with respect to their heart s potential center are unknown. As the number of access controllers and individuals within a facility increases, the number of interrogations grows rapidly. To mitigate data handling issues, the number of descriptors for a given individual must be minimized. In order to understand the extent that the data were able to generalize [47 49], discriminant functions were generated by training on the tasks individually and then block segmentation across tasks (Figure 17.19). If the features were completely invariant to anxiety state, then an operational enrollment and deployment scheme would be simpli ed. The results show a high degree of agreement of generalization across the tasks, except for the VR driving. VR driving is the highest stressed task. Upon review of the VR driving data, many of the subjects data still contained muscle exor noise that was not removed with the current lter (Figure 17.19).