# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 4 Biometrics Application: Results and Analysis
### Experimental Results with the Head Pose Database  
The Head Pose database (Figure 8) [59] includes 2790 images of faces taken from 15 individuals with pan and tilt variation angles from \(-90\) to \(+90\) degrees. For each individual, 2 sets with 93 different positions were captured [60].  
Figure 7: (a–f) The comparative recognition results changing the dimensionality of the transforming matrix for each given training number Tn on each data (ORL database).  
As can be observed in Table 4, SKLDNE performed better than the other seven methods, regardless of the variation in the training sample size. The maximal recognition rate of SKLDNE when \(Tn=130\) was up to 99.28%, while for other methods it was much lower. This reveals that, when the given training sample size for each class gets larger, SKLDNE can obtain much better results than other methods. Two more points can also be outlined. First, our supervised method with kernel weighting can notably enhance the class classification performance, but applying the kernel trick has no significant influence on PCA performance. Second, SKLDNE achieves optimal recognition rates at almost smaller number of dimensions as the recognition rate of SKLDNE retains the best results as the dimension varies from 14 to 30. Compared to the other techniques, SKLDNE preserves the more discriminative and local features of face images. It also preserves more local geometric relations of the within-class samples by nonlinear kernel mapping. It should be noted that linear methods such as LPP, LDA, LDNE, DNE, and UDP often fail to deliver good classification performance when face images are subject to complex nonlinear changes such as expression, lighting, pose and so on. Figure 9 indicates that the recognition implementations of all methods first sharply increase while the projected dimensions are added, and then, after obtaining the optimum, they tend to become stable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Database** & \multicolumn{6}{c}{**Head Pose**} \\ \hline Tn & **30** & **70** & **90** & **110** & **120** & **130** \\ \hline PCA & 66.21 & 63.69 & 50.16 & 79.73 & 83.6 & 82.67 \\  & (30) & (26) & (26) & (26) & (74) & (26) \\ \hline KPCA & 66.38 & 64.31 & 59.37 & 84.86 & 86.22 & 85.71 \\  & (30) & (70) & (30) & (90) & (22) & (62) \\ \hline UDP & 65.83 & 64.39 & 58.75 & 85.52 & 87.21 & 85.71 \\  & (6) & (22) & (34) & (98) & (94) & (78) \\ \hline LPP & 68.01 & 64.4 & 59.7 & 85.39 & 88.36 & 87.85 \\  & (30) & (82) & (26) & (90) & (62) & (50) \\ \hline LDA & 68.21 & 65.14 & 60 & 86.57 & 87.04 & 88.57 \\  & (6) & (18) & (22) & (98) & (98) & (46) \\ \hline DNE & 66.28 & 64.5 & 58.5 & 84.63 & 86.22 & 85.71 \\  & (30) & (70) & (30) & (90) & (74) & (62) \\ \hline LDNE & 69.7 & 66.2 & 59 & 96.9 & 98 & 98.02 \\  & (20) & (19) & (18) & (24) & (18) & (18) \\ \hline SKLDNE & **70.7** & **67.06** & **60.83** & **98.94** & **99.01** & **99.28** \\  & (30) & (18) & (22) & (22) & (18) & (14) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Maximum recognition accuracies (in percentage terms) of SKLDNE and other methods for the different number of training and testing images on Head Pose database and corresponding dimensions (shown in parentheses).  
Figure 8: A subset of some images of one subject from the Head Pose database [59].