# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 4 Biometrics Application: Results and Analysis
### Experimental Results with the Finger Vein Database. The finger vein database used in this project was collected from 51 individuals (male and female) who were aged between 21 and 56 [61]. 10 images were captured from each subject. Four fingers were used for capturing, including right and left middle finger and right and left index finger. There are 204 different fingers in the database, and the data consist of 2040 images in total, in which each finger image originally had a dimension of 480 \(\times\) 160 pixels. In our implementations, each image was resized to 32 \(\times\) 32. The captured images from one person can be seen in Figure 10.  
Figure 9: **(a–f)** Comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn in each dataset (Head Pose database). In this section, the performance of each technique followed by a maximal recognition rate was evaluated through changing the dimensionality of transformation matrix. The number of training samples \(Tn=1\), \(2\), \(3\), \(4\), \(5\), \(6\), \(7\) was chosen from the image gallery to make the training sample set, and the rest of images were selected for testing [62]. Furthermore, the PCA classifier (nearest neighbor NN using the Euclidean distance) was applied in the recognition phase, and the best recognition rates of each technique are indicated in Table 5.  
Based on the experiment results shown in Figure 11, our SKLDNE gained the best recognition rate among all different training numbers, which proves that it has an encouraging performance compared to other advanced methods. Regarding the small training sample size case, the SKLDNE method still showed that it performed significantly better than other techniques, as the maximal recognition accuracy rate of SKLDNE in training number 2 was almost 5% more than PCA, KPCA, UDP, LPP, and DNE, and 1.2% more than LDNE. Our SKLDNE was always able to represent its optimal embedding space with a lower value of dimensions in comparison with the other seven techniques. For example, SKLDNE for \(Tn=7\) achieved 100% recognition accuracy in the smallest value of projected dimensions (26). This conveys that our approach is more effective, due to its significant characteristic that it can not only represent nonlinear and complex variations in of images, but can also model both locality of LPP and discrimination of DNE simultaneously. This fact demonstrates the good performance of our proposed method. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multicolumn{2}{l}{**Database**} & \multicolumn{6}{c}{**Finger Vein**} \\ \hline \multicolumn{2}{l}{Tn} & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline \multirow{2}{*}{PCA} & 79.66 & 89.37 & 94.85 & 96.3 & 96.41 & 99 & 99.54 \\  & (30) & (34) & (34) & (26) & (26) & (26) & (27) \\ \hline \multirow{2}{*}{KPCA} & 79.33 & 88.75 & 94.57 & 96.33 & 96.4 & 99.2 & 99.5 \\  & (30) & (30) & (30) & (30) & (26) & (26) & (27) \\ \hline \multirow{2}{*}{UDP} & 80 & 90.75 & 95.85 & 96.8 & 97 & 99 & 99.5 \\  & (30) & (30) & (30) & (34) & (30) & (34) & (30) \\ \hline \multirow{2}{*}{LPP} & 79.66 & 89.5 & 94.85 & 96.83 & 96.6 & 99 & 99.56 \\  & (30) & (22) & (34) & (26) & (22) & (34) & (34) \\ \hline \multirow{2}{*}{LDA} & 79.66 & 91.75 & 96.71 & 97.16 & 98.2 & 99.5 & 99.55 \\  & (30) & (26) & (30) & (30) & (30) & (22) & (29) \\ \hline \multirow{2}{*}{DNE} & 81 & 90.12 & 95.42 & 97 & 96.8 & 99.15 & **100** \\  & (90) & (90) & (62) & (86) & (66) & (54) & (86) \\ \hline \multirow{2}{*}{LDNE} & 80.75 & 94.17 & 96.85 & 97.5 & 96.4 & 99.25 & 99.2 \\  & (86) & (38) & (62) & (76) & (74) & (66) & (42) \\ \hline \multirow{2}{*}{SKLDNE} & **81.22** & **95.38** & **97.71** & **98.5** & **99.2** & **99.75** & **100** \\  & (54) & (26) & (26) & (34) & (34) & (26) & (26) \\ \hline \end{tabular}
\end{table} 
Table 5: Maximum recognition accuracies (in percentage terms) of SKLDNE and other methods for the different number of training and testing images on Finger Vein database and corresponding dimensions (shown in parentheses).