## 3 Experiments
### Face Recognition Results  
We compared the proposed method with other methods dealing with the SSPP problem (i.e., WIM, ICR, E(PC\({}^{2}\))A+, SPCA+, (2D)\({}^{2}\)PCA, SLC, MVI, and SRGES methods). The proposed method, WIM, and SRGES generated as many images as the number of variations contained in the auxiliary set. With the ICR, the number of generated images depended on the \(k\) neighbors in the training set and the feature extraction method used by each database. In E(PC2)A+, the half-, first-, and second-order projected images of each neutral image were used as the training set. In SPCA+, seven images were enlarged from different \(n\)-order singular values for each neutral image in the training set. In (2D)\({}^{2}\)PCA, an image was generated using a two-directional PCA in the row and column directions of the 2D images. In SLC, 11 images from the neutral image were added to the training set, which included symmetric images and linear combinations of virtual images. In MVI, four low-resolution images (size 40 \(\times\) 40, 26 \(\times\) 26, 20 \(\times\) 20, and 16 \(\times\) 16) are generated from the neutral image and various scaling factors (i.e., 2, 3, 4, 5, respectively). In this study, the face recognition performance of all methods was evaluated based on the given criteria. First, we measured the change in the face recognition rate according to the degree of variation in each database. Both databases contained similar facial expression variations, but they differed in the intensity of the facial expressions. In the Bosphorus database, the AUs were captured at their given peak intensity levels. In the RaFD database, there were large deviations in the intensities of expressions according to subject. Thus, the RaFD database was closer to the real \begin{table}
\begin{tabular}{l c c} \hline \hline
**Expression** & **Bosphorus** & **RaFD** \\ \hline Neutral & & \\ Afraid & & \\ Angry & & \\ Disgusted & & \\ Sad & & \\ Smiling (smiling) & & \\ Surprise (scream) & & \\ Contemptuous & & \\ \hline No. of subjects & 58 & 67 \\ No. of images per subject & 7 & 8 \\ Index of neutral face images & 5 & 6 \\ No. of testing images & 348 & 469 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of each facial expression database. world than the Bosphorus one. Second, the face recognition performance was analyzed according to unsupervised and supervised learning methods. An unsupervised learning-based PCA [24] and supervised learning-based discriminant common vector (DCV) [40] were used to extract the features for face recognition. PCA extracted \((\mathcal{N}+\mathcal{N}^{\prime}-1)\) features, including the number of images of training data (\(\mathcal{N}\)) and the number of enlarged images (\(\mathcal{N}^{\prime}\)) from itself. DCV extracted \((c-1)\) features, where \(c\) was the total number of classes, regardless of the number of images. In the face recognition experiment, the recognition rates were measured using the maximum number of features extracted from each method. If a given set had been modeled properly, it could be expected to show high performance, regardless of the two methods. When evaluating the face recognition performance, the one nearest-neighbor rule was used with the \(l_{2}\) norm as a classifier. In this study, two protocols for face recognition were used [41]: \"_Closed Set_\" and \"_Open Set_\", according to the auxiliary set. These are described as follows:  
* _Closed set_: In this case, all images were collected under similar conditions. Thus, all images belonged to the same database. In the experiment, the database was divided into a face recognition set and an auxiliary set. The face recognition set consisted of training and test sets. Neutral images for each class used to generate images were included in the training set, and the remaining images containing only variations were used as the test set.