# Mmpal _sciences_
## 4 Experiments and Results
### Experiments on the AR Database  
The AR database contains 3276 images of 126 people, which has an average of 26 per person, collected in two different time periods, including different expressions, illumination, and occlusion changes. The experiment was deployed in the following way and selected 100 individuals (50 males and 50 females) from the AR database as subjects. Eight face images per person in 100 objects were selected as training samples, one of which was not occluded and had no illumination change. Seven of them contained occlusion or illumination factors, as shown in Figure 6a. Testing set I is composed of 300 face images with normal light, strong light on the left, and strong light on the right, as shown in Figure 6b. Testing set II is composed of 300 face images with sunglasses occlusion mixed with normal light, strong light on the left and strong light on the right, as shown in Figure 6c. Testing set III is composed of 300 face images with scarf enclosures that contain normal light, light on the left, and strong light on the right, as shown in Figure 6d. All images were cut and aligned before the experiment. In the selection of experimental data, testing sets I, II, and III contain common sunglasses, scarves, and posed face occlusions, respectively, in a real uncontrolled environment, and strong illumination makes them more in line with the real scene. In order to verify that the model can effectively deal with occluded faces, we compared the face recognition methods commonly used in ESRC, NNAODL, PCANet, 2 DPCANet, and L1-2D2 PCANet, as shown in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Positive Samples**} & \multicolumn{2}{c}{**Negative Samples**} \\ \cline{2-5}  & **Training Time (s)** & **Testing Time (s)** & **Training Time (s)** & **Testing Time (s)** \\ \hline PCANet [14] & 454.83 & 0.31 & 499.48 & 0.30 \\
2 DPCANet [30] & **374.07** & 0.23 & **404.80** & 0.23 \\ L1-2D2 PCANet [19] & 554.81 & 0.17 & 577.59 & 0.18 \\ MMPCANet & 493.03 & **0.16** & 512.69 & **0.17** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance on CelebA dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Positive Samples** & **Negative Samples** \\ \hline ESRC [9] & 89.30 & 86.40 \\ NNAODL [10] & 96.09 & 95.58 \\ PCANet [14] & 95.20 & 94.93 \\
2 DPCANet [30] & 98.02 & 96.33 \\ L1-2D2 PCANet [19] & 97.58 & 97.50 \\ MMPCANet & **99.07** & **98.49** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average Recognition Rate (%) on CelebA dataset. Figure 6: Some examples of the AR database. Eight face images per person were selected as training samples, one of which was not occluded and had no illumination change. Seven of them contained occlusion or illumination factors, as shown in (**a**). Testing set I is composed of 300 face images with normal light, strong light on the left, and strong light on the right, as shown in (**b**); testing set II is composed of 300 face images with sunglasses occlusion mixed with normal light, strong light on the left, and strong light on the right, as shown in (**c**); testing set III is composed of 300 face images with scarf enclosures that contain normal light, light on the left, and strong light on the left, as shown in (**d**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Testing Set I** & **Testing Set II** & **Testing Set III** & **Avg.** \\ \hline ESRC [9] & 91.05 & 89.14 & 84.64 & 88.27 \\ NNAODL [10] & 95.74 & 92.44 & 91.69 & 93.29 \\ PCANet [14] & 93.27 & 90.48 & 87.66 & 90.47 \\
2 DPCANet [30] & 95.04 & 90.89 & 92.90 & 92.94 \\ L1-2D2 PCANet [19] & 96.05 & 95.88 & 94.43 & 95.45 \\ MMPCANet & **98.95** & **96.56** & **97.23** & **97.58** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average Recognition Rate (%) on AR database. The experimental results show that the recognition rates of the original algorithm and other methods are lower than our method.