## 3 Experiments
### Face Recognition Results
This method had the same variations (\"expression\") in both face recognition and auxiliary sets;
* _Open set_: This case used a separate auxiliary set from a given database to demonstrate the superiority of the proposed method. The training and test sets were collected under similar conditions. However, the auxiliary set was taken in environments different from those. The face recognition set was constructed in the same way as in the \"_Closed Set_\" case, and neutral images were used to enlarge the others. Both face recognition and auxiliary sets included \"expression\" variations. However, the types of detailed variations could be different. First, we divided the given databases into face recognition and auxiliary sets. A total of 30 subjects from all subjects in each database were used for the face recognition set, and the others were used for the auxiliary set. Among the 210 and 240 images for 30 subjects in the Bosphorus and RaFD databases, respectively, neutral images were used as training data to construct PCA and DCV feature spaces for face recognition, and variational images were generated using the proposed methods from these images to enlarge the training set. Table 2 shows the face recognition results for the \"_Closed Set_\" protocol. In the experimental results, the proposed method, WIM, and (2D)2 PCA presented similar facial-recognition results within the same database, regardless of the feature-extraction manner. The other methods had a face recognition rate difference of up to 21.11% between each manner. Additionally, the proposed method and WIM showed high performance in the face recognition results according to the degree of variation by database. For the rest of the methods, the face recognition performance decreased by more than 15.87\(\sim\)33.17% as the degree of variation increased. Figure 6 shows the recognition rates for a different number of DCV features. The proposed method gives a recognition rate of 96.11% and 93.33%, with 29 features for the Bosphorus and RaFD databases, respectively. As can be seen from Figure 6, the proposed method shows a comparable or better recognition performance to the other methods, regardless of the number of features. Finally, we confirmed that the proposed method was excellent in the absolute comparison of face recognition rates for both databases. Because the proposed method consistently showed high face recognition performance regardless of the various criteria, it could be inferred that a new image was generated by reflecting the various variations from the given neutral images. Generally, the basic emotion group consists of angry, disgusted, afraid, sad, smiling, and surprised [42]. For the \"_Open Set_\" protocol, the auxiliary set containing six defined facial expressions consists of the AR [43], CK+ [44], Jaffe [45], PF07 [46], and Yale [47] databases. Additionally, it included various races and genders. To measure the degree of change from the variations, only subjects without glasses (occlusion) were used to construct the auxiliary set. The selected subjects had images of both neutral and facial expressions. The AR database contained images from 85 subjects (37 males and 48 females) of different races [43]. We selected four facial expressions: neutral, angry, smiling, and screaming. The CK+ database contained 84 subjects from many different races. Image sequences contained changes in facial expressions over time. The neutral image at the start time and the facial expression image at the end time comprised the auxiliary set. We used seven facial expressions (i.e., neutral, angry, afraid, disgusted, sad, smiling, and surprised), except for \"contemptuous.\" The Jaffe database included 10 subjects (only females) of Asian ethnic groups. Seven facial expressions of each subject were taken (e.g., neutral, angry, afraid, disgusted, sad, smiling, and surprised).