# Robust Face Recognition Based on a New Supervised Kernel Subspace Learning Method
## 4 Biometrics Application: Results and Analysis
### Classification Performance and Computational Cost  
In this section, by means of a new group of experiments, we evaluated SKLDNE performance through changing k-neighborhood variation _Wk_ (from 1 to 30 with a scale of 2). The number of training samples selected for each database were \(Tn\) = 4, 5, 6, 7, 8, 15, 16, 17 in Sheffield, \(Tn\) = 2, 6, 7, 8, 9 in Yale, \(Tn\) = 5, 6, 7, 8, 9 in ORL, \(Tn\) = 120, 130, 140, 150, 160 in Head Pose, \(Tn\) = 5, 6, 7, 8, 9 in Finger Vein, and \(Tn\) = 7, 8, 9, 10, 11 in Finger Knuckle databases. It should be noted that the rest of each class in each dataset was used for testing. The training number samples were randomly selected. The maximum  
Figure 13: (**a–i**). Comparative recognition results changing the dimensionality of the transformation matrix for each given training number Tn (Finger Knuckle database). recognition rates of SKLDNE in comparison with _Wk_ for different numbers of training samples are indicated in Figure 14a-f. It can be seen that the classification performance became better as the number of training samples increased. The classification performance of SKLDNE improved first with a rise of _Wk_ until almost _Wk_ = 9 in the Sheffield and Head Pose, and then it decreased dramatically. In the Yale, ORL, Finger Vein, and Finger Knuckle datasets, it can easily be observed that the recognition performance of SKLDNE enhanced rapidly when _Wk_ varied from 1 to 7 in Yale, 1 to 10 in ORL, 1 to 9 in Finger Vein, from 1 to 6 in Finger Knuckle, and then it decreases when _Wk_ became larger, since large values of  
Figure 14: (**a–f**). Maximum recognition rate of SKLDNE versus Wk for different number of training samples on Sheffield, Yale, ORL, Head Pose, Finger Vein and Finger Knuckle databases. k-neighborhood variable _Wk_ have an effect on creating the weight adjacent matrix. It has already been proven that the k-neighborhood selected for data point might contain more outliers belonging to other classes at a large number of _Wk_ when a dataset includes many classes with a small number of samples for each class. Thus, the constructed adjacent weight matrix does not have sufficient discrimination for image recognition [15]. The experiment for analyzing computational cost was carried out on an Intel(R) Core i5-4200U CPU, 2.3 GHz, 10 GB RAM machine using MATLAB (R2016, Natick, MA, USA). The computational costs of the different classification methods using the Yale data base are listed in Table 7.  
From the results shown in Table 7, it can be observed that the proposed SKLDNE was faster than its main competitors, such as LDNE, DNE, and LPP. The processing times of PCA, KPCA, UDP, and LDA were lower. However, the recognition rate results illustrate that these methods were much less accurate than the SKLDNE method. Now, to have a more reliable comparison, we briefly compare our recognition results of the proposed method with previously published works, including a deep learning method named Deep Belief Networks (DBNs) [65; 66] with a traditional multilayer perceptron model (MLP) [66] in the used facial expression databases, i.e., the JAFFE Database [67]. As a deep learning method, DBNs have an unsupervised feature learning ability. The JAFFE database includes 10 individuals (Japanese women) with 7 different expressions, and has around 3 or 4 images for each expression. There are 213 images in total in this database. Each image has a resolution pixel of 256 \(\times\) 256. In detail, we divided all image samples into 10 parts, 90% of which were applied for training, and the remaining were applied for testing. Table 8 illustrates the recognition performance comparisons in the JAFFE database when dealing with three different image resolutions of 16 \(\times\) 16, 32 \(\times\) 32, and 64 \(\times\) 64. We can clearly see that the proposed SKLDNE method achieved the best recognition performance (100% in all cases), in comparison with other previously reported results [66], which are much lower.