# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 4 Biometrics Application: Results and Analysis
### Experimental Results with the ORL Database  
The ORL face database [56] includes ten diverse grayscale images taken from 40 different individuals [57]. All 10 face images of each subject were captured at different times, with changes in the lighting, facial details (with glasses or no glasses) or facial expressions (smiling/not smiling, open/closed eyes,), against a dark homogeneous background, and with straight and frontal views. The size of all images is equal to 92 \(\times\) 112 pixels in PGM format. The images were captured in 40 directories [58]. It should be noted that preprocessing was used and all original images were already cropped and resized. In this project, the size of 32 \(\times\) 32 pixels was chosen for all ORL images. Figure 6 illustrates three different subjects (each with 10 images) from the ORL database. Figure 5: (a–e). The comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn on each dataset (Yale Face database). In our experiments, the number of training samples \(Tn\) = 1, 4, 3, 4, 5, 6, 7, 8 were chosen from the dataset related to each subject to make the training sample set. The other numbers of images are applied as a testing sample set. As already mentioned, PCA was used in the classification phase in all methods. The maximal average accuracy (in percentage terms) and its corresponding dimension, followed by the alteration in the training sample sizes, are illustrated in Table 3. It can be observed in this yable and in Figure 7a-f that SKLDNE generally outperformed LDNE, whether the number of training sample size was small or not, in almost smaller numbers of dimensions. Moreover, as a supervised method, SKLDNE also significantly outperformed other techniques (KPCA, LPP, DNE, UDP, and LDA) regardless of the change in the training sample size. Compared to other techniques, SKLDNE performed better in small training sample size case. Furthermore, when the training number was equal to 8, SKLDNE had a zero error rate compared to that of PCA (4.1%), KPCA (3.5%), UDP (4%), LPP (3.5%), LDA (4%), DNE (3.75), and LDNE (3.5%). SKLDNE can simultaneously discover interclass and intraclass geometrical information, and have more nonlinear data representation, locality preservation, and discriminating power than other techniques. Therefore, SKLDNE does have merit over other techniques in terms of resolving classification problems in face recognition. This characteristic of SKLDNE in small sample size cases is indeed important to improve the recognition rate in practice, since face recognition is commonly a small sample size problem. Normally, a small number of images of each person is accessible in many real-world tasks. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Database** & \multicolumn{6}{c}{**ORL Face**} \\ \hline Tn & **1** & **4** & **5** & **6** & **7** & **8** \\ \hline PCA & 78.75 & 85.41 & 87.5 & 95.62 & 95.83 & 95.9 \\  & (30) & (30) & (26) & (20) & (10) & (10) \\ \hline KPCA & 81.56 & 87 & 89 & 96.2 & 96.66 & 96.25 \\  & (46) & (54) & (66) & (34) & (34) & (20) \\ \hline UDP & 80 & 86.66 & 89.5 & 94.75 & 96.6 & 96 \\  & (54) & (90) & (98) & (38) & (18) & (14) \\ \hline LPP & 80.62 & 87.5 & 90 & 95 & 95.8 & 97.5 \\  & (58) & (86) & (94) & (34) & (30) & (62) \\ \hline LDA & 80.93 & 87.91 & 90 & 96.25 & 95.83 & 96 \\  & (54) & (34) & (38) & (22) & (34) & (18) \\ \hline DNE & 81.56 & 87.08 & 89 & 96.2 & 96.66 & 96.25 \\  & (46) & (54) & (66) & (34) & (34) & (10) \\ \hline LDNE & 85 & 92 & 92 & 95.6 & 95 & 96.5 \\  & (26) & (62) & (78) & (30) & (24) & (54) \\ \hline SKLDNE & **85.93** & **93.33** & **94** & **96.87** & **97.5** & **100** \\  & (38) & (61) & (50) & (66) & (22) & (18) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum recognition accuracies (in percentage terms) of SKLDNE and other methods for the different number of training and testing images in the ORL Face database and corresponding dimensions (shown in parentheses).