## 5 Experiments
### Experiments on the Yale Face Dataset  
In the experiments, we first consider the Yale face dataset which contains 165 gray scale images for 15 individuals with 11 images per category. Each individual contains one different facial expression or configuration: Left-light, center-light, right-light, w/glasses, w/no glasses, happy, sad, normal, surprised, sleepy and wink, as shown in Figure 1(a). Each image has \(24\times 24\) pixel resolution, and is resized to 576-dimensional vectors with normalization for representation. Following the setting in [19], six images of each individual are randomly selected for training and the rest are used for testing. In addition, the number of dictionary atoms is set to \(15\times 4+60=120\), which means four class-specific atoms for each individual and 60 shared atoms for all the individuals. The parameters of our LPLC-HDL on the Yale face dataset can be seen in Table 1.  
To acquire a stable recognition accuracy, we operate LPLC-HDL over 30 times rather than 10 times with independent training/testing splits. The comparison results on the Yale face dataset are listed in Table 2. Since the variations in terms of facial expression are complex, the variations in the testing samples cannot be well represented via directly using the training data. Hence SRC has worse accuracy than the other dictionary learning methods. We can also see that the hybrid dictionary learning methods including DL-COPAR [16],  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Yale** & **Ext. YaleB** & **LFW** & **Caltech-101** & **102 Flowers** \\ \hline \(\lambda\) & \(1\times 10^{-1}\) & \(1\times 10^{-1}\) & \(1\times 10^{-2}\) & 3 & \(2\times 10^{-1}\) \\ \(\gamma\) & \(1\times 10^{4}\) & \(2\times 10^{3}\) & \(5\times 10^{3}\) & \(3\times 10^{2}\) & \(1\times 10^{4}\) \\ \(\eta\) & \(1\times 10^{-3}\) & \(1\times 10^{-3}\) & \(1\times 10^{-3}\) & \(1\times 10^{1}\) & \(1\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameters of the proposed LPLC-HDL method on each dataset.  
Figure 2: The example images from the face datasets.  
LRSDL [17] and CLSDDL [19] outperform the remaining competing approaches, and the proposed LPLC-HDL method achieves the best recognition accuracy of 97.01%, which illustrates that our method can distinguish the shared and class-specific information of face images more appropriately.  
We further illustrate the performance of LPLC-HDL on face recognition accuracy with different sizes of the shared and class-specific dictionaries, as shown in Figure 3. From it we can see that a higher recognition accuracy on the Yale face dataset can be obtained by increasing the atom numbers of both the shared and class-specific dictionaries. Besides, Figure 3 also shows that when the number of the class-specific atoms is few, the recognition accuracy is sensitive to the number of the shared atoms, as the large shared dictionary is harmful to the discriminative power of the class-specific dictionary in this case. However, increasing the number of the class-specific atoms beyond the particular number of training samples of each class brings no notable increase in recognition accuracy. Considering that the large dictionary will slow down both the training time and the testing time, the atom numbers of the shared and class-specific dictionaries are not set to big values in the experiments.