# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 4 Biometrics Application: Results and Analysis
### Experimental Results with the Sheffield Face Database
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Database** & \multicolumn{10}{c}{**Sheffield Face**} \\ \hline
**Tn** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **15** & **16** & **17** \\ \hline \multirow{3}{*}{**PCA**} & 45.1 & 47.94 & 49.68 & 49 & 49.64 & 51.15 & 52.5 & 54.54 & 85.5 & 93 & 92 \\  & (18) & (18) & (18) & (18) & (30) & (26) & (30) & (26) & (18) & (28) & (10) \\ \hline \multirow{3}{*}{**KPCA**} & 45.2 & 48.2 & 50.31 & 50.33 & 50.7 & 51.92 & 54.15 & 55.9 & 87.5 & 93 & 92 \\  & (18) & (22) & (30) & (38) & (42) & (58) & (50) & (69) & (38) & (30) & (14) \\ \hline \multirow{3}{*}{**UDP**} & 45.33 & 48.1 & 48.43 & 51.66 & 50.71 & 51.9 & 55.41 & 57.27 & 87 & 95 & 92.5 \\  & (10) & (22) & (30) & (30) & (45) & (66) & (54) & (50) & (90) & (86) & (14) \\ \hline \multirow{3}{*}{**LPP**} & 45.55 & 48.2 & 52.81 & 50.66 & 56.07 & 52.3 & 54.16 & 55.9 & 90 & 93.33 & 95 \\  & (14) & (26) & (12) & (34) & (38) & (54) & (46) & (62) & (74) & (42) & (34) \\ \hline \multirow{3}{*}{**LDA**} & 45.2 & 50.29 & 48.43 & 58.66 & 56.07 & 59.23 & 60 & 61.36 & 92.5 & 93 & 97.5 \\  & (18) & (26) & (14) & (34) & (22) & (6) & (42) & (50) & (22) & (30) & (18) \\ \hline \multirow{3}{*}{**DNE**} & 45.2 & 48.23 & 50.31 & 51.33 & 51.78 & 51.9 & 54.58 & 56.36 & 87.5 & 93.33 & 92.5 \\  & (18) & (34) & (14) & (74) & (58) & (42) & (74) & (78) & (38) & (30) & (20) \\ \hline \multirow{3}{*}{**LDNE**} & 45.27 & 50.58 & 56.87 & 58.66 & 65 & 73.07 & 76.66 & 76.81 & 90 & 96.1 & 97.5 \\  & (22) & (9) & (14) & (14) & (14) & (34) & (18) & (14) & (22) & (14) & (18) \\ \hline \multirow{3}{*}{**SKLDNE**} & **46.38** & **52.94** & **59.06** & **62.66** & **69.64** & **78.46** & **83.75** & **80.45** & **93.75** & **98.33** & **100** \\  & (10) & (10) & (14) & (10) & (14) & (30) & (10) & (10) & (34) & (10) & (10) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum recognition accuracies (in percentage terms) of supervised kernel locality-based discriminant neighborhood embedding (SKLDNE) and other methods for the different numbers of training and testing images on the Sheffield Face and corresponding dimensions (shown in parentheses). Figure 2: A sample of pre-cropped face images in the Sheffield Face database [51]. much lower for other methods. SKLDNE can effectively yield an optimal embedding subspace that finds substantial submanifolds-based structure with lower dimensionality. The within-class local structure, which is very important for face recognition, can be preserved simultaneously in a nonlinear kernel feature space. SKLDNE can solve the \"out-of-sample\" problem and the \"overlearning of locality\" problem in manifold learning, which other aforementioned methods often face. Therefore, based on these characteristics, it can be concluded that the recommended SKLDNE technique is a promising technique to be used for dimensionality reduction, with a very satisfactory performance in classification when dealing with high-dimensional data. Figure 3: \(Cont.\)