## 8 Results  
The three classifiers are trained and tested following the offline procedure. The main aim of applying three classifier models is to select the model that is best suited for biometrics user verification. A total of 30% of the collected database was allocated for testing. As the system is designed to be used for user's verification, the user should input the user name first and then the user should enter the biometrics identity. A cross-validation process is performed in order to select the parameters values for each of the three classifier applied in this research. The same dataset is used to train and test each classifier. Table 2 shows the selected parameter for each classifier used in the training and testing of the data. The best model for each classifier type of the three classifiers was selected based on its accuracy results. The testing results are statistically studied and compared to find the best classifier model (KNN, LDA, and Ensemble classifier). The average testing accuracy is calculated as an average of thirty trials. The Ensemble classifier algorithm produced the highest testing accuracy of 98.5%. The LDA classifier provided a testing accuracy equal to 98.3%. Furthermore, the KNN classifier provided a mean value of the testing accuracy equal to 97.4%. Figure 5 presents the results. \begin{table}
\begin{tabular}{l c} \hline \hline
**k-Nearest Neighbors** & \\ \hline
**Number of neighbors** & 2 \\ \hline
**Distance metric** & Minkowski \\ \hline
**Distance Weight** & Inverse \\ \hline
**Exponent** & 0.57 \\ \hline
**Linear Discriminant Analysis** & \\ \hline
**Delta** & 0.01 \\ \hline
**Gamma** & 0.7 \\ \hline
**Discriminant Type** & PseudoLinear \\ \hline
**Ensemble Classifier** & \\ \hline
**Weak Learner** & Decision Tree \\ \hline
**Method** & GentleBoost \\ \hline
**Number of Learning Cycles** & 11 \\ \hline
**Learning Rate** & 0.95 \\ \hline
**Minimum Leaf Size** & 22 \\ \hline
**Maximum number of Split** & 1 \\ \hline
100.00\% & \\
98.00\% & \\
96.00\% & \\
94.00\% & \\
92.00\% & \\
90.00\% & \\
88.00\% & \\
86.00\% & \\
84.00\% & \\
82.00\% & \\
80.00\% & \\ \hline \end{tabular}
\end{table} 
Table 2: Selected parameters for the classifiers. Figure 5: Average Testing Accuracy. For performance analysis of the system, the accuracy, false acceptance rate (FAR), and false rejection rate (FRR) for each case are calculated. The FAR gives the percentage of accepted unauthorized users attempted to spoof the system. A system's FAR typically is stated as the ratio of the number of false acceptances divided by the number of verification attempts. The FRR on the opposite side provides the percentage of rejected attempts of authorized users tried to access the system. A system's FRR is calculated as the ratio of the number of false recognitions divided by the number of verification attempts. For biometrics verification applications, the registered users need to declare their identity, which is a user name in this particular application, along with the biometric identifier. The authentication system then compares the input identity with the stored template in a database of various claimed identities to confirm or deny the authenticity claims [47]. As such, the verification mode is a binary classification. The performance of the verification system is evaluated by both FAR and FRR. The values of FAR and FRR are calculated in all verification scenarios and for each type of classifiers presented in this research. For the KNN classifier, the average value of FAR is 0.2%, which indicates that none of the users are able to access any other user even by mimicking the hand actions and the FRR is 2.9% which means out of 100 user, 2.9 users were not able to access the system due to a deviation in the hand actions that represents the password of their own. For the LDA classifier, the FAR is 0.3% and FRR is 1.9%. While, applying the Ensemble Classifier resulted in FAR of 6.3% and FRR of 1%. Figure 6 shows the FAR and FRR of the three classifiers.