**5.2 Experimental results using the YALE face image database**

In this last experiment, the YALE face database was used. It contains 15 people, each of them were doing 11 poses. The poses were taken in various kinds of lighting (left lighting 154 Principal Component Analysis

in 100% recognition rate, using 8 dimension resulted in 97% recognition rate, and 100% recognition rate was yielded from experimental results using more than 9 dimensions, as

Fig. 6. Experimental Results on ORL Face Image Database Using 8 Training Set

Fig. 7. Experimental Results on ORL Face Image Database Using 9 Training Set

to the number of dimensions used [Arif et al., 2008b].

**5.2 Experimental results using the YALE face image database** 

The maximum recognition rate for all scenarios can be seen in Table 2. This table shows that the more number of training set used, the higher recognition rate achieved, whereas the first maximum recognition rate tended to occur on the lower dimension inversely proportional

In this last experiment, the YALE face database was used. It contains 15 people, each of them were doing 11 poses. The poses were taken in various kinds of lighting (left lighting

shown in Figure 7 [Arif et al., 2008b].

and center lighting), various expressions (normal, smiling, sad, sleepy, surprising, and wink) and accessories (wearing or not wearing glasses) [Yale Center for Computational Vision and Control, 2007] as shown in Figure 8.



Fig. 8. Face Sample of Images of YALE Database

The experiments were conducted for 6 scenarios, for each scenario, 5, 6, 7, 8, 9, and 10 training set were used. The rest of each data sample for every experiment, i.e. 6, 5, 4, 3, 2 and 1, were used as testing set as listed in Table 3 [Arif et al., 2008b].


Table 3. The Scenario of the YALE Face Database Experiment

The Maximum Non-Linear Feature Selection of Kernel Based on Object Appearance 157

number of dimensions the recognition rate decreased. But when the number of dimensions used was more than 14, experimental results yielded its maximum rate, which is 98.33% as

Fig. 10. Experimental Results on YALE Face Image Database Using 7 Training Set

Fig. 11. Experimental Results on YALE Face Image Database Using 8 Training Set

In the last three scenarios as seen in Figure 11, 12, and 13, experimental results have shown that the recognition rate also tended to increase when the number of dimensions used was less than 7, whereas experimental results that used more than 8 dimensions achieved 100%

seen in Figure 10 [Arif et al., 2008b].

recognition rate [Arif et al., 2008b].

In the first scenario, 5 training sets were used, where the rest of the YALE data experiment was used for testing. In this scenario, the number of dimensions used was 75. The completed experimental results can be seen in Figure 8. This figure shows that the number of recognition rate increased significantly when less than 9 dimensions were used, which were 16.67% until 92.22%. Whereas the maximum recognition rate occurred when 13, 14, and 15 dimensions were used, that was 94.44% [Arif et al., 2008b]. For experimental results using more than 16 dimensions, the recognition rate fluctuated insignificantly as seen in Figure 8.

Fig. 8. Experimental Results on YALE Face Image Database Using 5 Training Set

The experimental results of the 2nd scenario were shown in Figure 9. The recognition rate increased from 22.67% until 97.33% when using less than 10 dimensions, recognition rate decreased insignificantly when using 16 dimensions, and recognition rate tended to be stable around 97.33% when experiments used more than 17 dimensions, [Arif et al., 2008b].

Fig. 9. Experimental Results on YALE Face Image Database Using 6 Training Set

Similarly, it occurred in the 3rd scenario. In this scenario, the recognition rate increased significantly when the number of dimensions was less than 13, though on the certain 156 Principal Component Analysis

In the first scenario, 5 training sets were used, where the rest of the YALE data experiment was used for testing. In this scenario, the number of dimensions used was 75. The completed experimental results can be seen in Figure 8. This figure shows that the number of recognition rate increased significantly when less than 9 dimensions were used, which were 16.67% until 92.22%. Whereas the maximum recognition rate occurred when 13, 14, and 15 dimensions were used, that was 94.44% [Arif et al., 2008b]. For experimental results using more than 16 dimensions, the recognition rate fluctuated insignificantly as seen in Figure 8.

Fig. 8. Experimental Results on YALE Face Image Database Using 5 Training Set

Fig. 9. Experimental Results on YALE Face Image Database Using 6 Training Set

Similarly, it occurred in the 3rd scenario. In this scenario, the recognition rate increased significantly when the number of dimensions was less than 13, though on the certain

The experimental results of the 2nd scenario were shown in Figure 9. The recognition rate increased from 22.67% until 97.33% when using less than 10 dimensions, recognition rate decreased insignificantly when using 16 dimensions, and recognition rate tended to be stable around 97.33% when experiments used more than 17 dimensions, [Arif et al., 2008b].

number of dimensions the recognition rate decreased. But when the number of dimensions used was more than 14, experimental results yielded its maximum rate, which is 98.33% as seen in Figure 10 [Arif et al., 2008b].

Fig. 10. Experimental Results on YALE Face Image Database Using 7 Training Set

In the last three scenarios as seen in Figure 11, 12, and 13, experimental results have shown that the recognition rate also tended to increase when the number of dimensions used was less than 7, whereas experimental results that used more than 8 dimensions achieved 100% recognition rate [Arif et al., 2008b].

Fig. 11. Experimental Results on YALE Face Image Database Using 8 Training Set

The Maximum Non-Linear Feature Selection of Kernel Based on Object Appearance 159

Table 4. The YALE Face Database Recognition Rate using Maximum Feature Value Selection

ORL 5 79.50 86.5 94.00 97.50

YALE 5 81.11 84.44 86.67 94.44

**6. The maximum value selection of kernel linear preserving projection as** 

Kernel Principal Component Analysis as appearance method in feature space yields global structure to characterized an object. Besides global structure, local structure is also important. Kernel Linear Preserving Projection as known as KLPP is method used to preserve the intrinsic geometry of the data and local structure in feature space [Cai et al., 2005; Cai et al.,, 2006; Kokiopoulou, 2004; Mauridhi et al., 2010]. The objective of LPP in

<sup>2</sup> min ( ) . *ij i j ij*

<sup>2</sup> ( )

*t i j*

>0, but it is sufficiently small compared to the local neighborhood radius.

  

*x x*

*otherwise*

*y y S* (24)

 

(25)


Minimizing the objective function ensures the closeness between points that is located in the

PCA LDA/QR LPP/QR

6 83.13 91.25 94.37 99.38 7 85.00 92.50 95.83 100.00

6 85.33 86.67 94.67 97.33 7 95.00 95.00 96.67 98.33

1st 5 94.444 13 2nd 6 97.333 10 3rd 7 98.333 9 4th 8 100 8 5th 9 100 7 6th 10 100 7

The First Maximum

Recognition Rate Dimension

The Maximum Recognition Rate (%)

The Maximum Value Selection of Kernel Principal Component Analysis

Scenario Number of Training

Method of Non linear Function based on KPCA

Training Set

Table 5. The Comparative Results for Face Recognition Rate

**extension of kernel principal component analysis** 

In this case the value of *Si,j* can be defined as

Where

*ij*

*S e*

 

feature space is written in the following equation [Mauridhi et al., 2010]

0

*i j x x*

 

Database Number of

Sample for Each Person

Fig. 12. Experimental Results on YALE Face Image Database Using 9 Training Set

Fig. 13. Experimental Results on YALE Face Image Database Using 10 Training Set

As seen in Table 4, the maximum recognition rate for 5, 6, 7, 8, 9, and 10 training sets were 94.444%, 97.333%, 98.333%, 100%, 100% and 100% respectively. Based on Table 4, the maximum recognition rate increased proportionally to the number of training sets used. The more number of training set used, the faster maximum recognition rate is reached [Arif et al., 2008b].

The experimental results of the 1st, 2nd, and 3rd scenarios were compared to other methods, such as PCA, LDA/QR, and LPP/QR as seen in Table 5, whereas for the 4th and 5th scenarios were not compared, since they have achieved maximum result (100%). The recognition rate of 5, 6, and 7 training set, for both on the ORL and the YALE face database, "The Maximum Value Selection of Kernel Principal Component Analysis", outperformed the other methods.

158 Principal Component Analysis

Fig. 12. Experimental Results on YALE Face Image Database Using 9 Training Set

Fig. 13. Experimental Results on YALE Face Image Database Using 10 Training Set

al., 2008b].

As seen in Table 4, the maximum recognition rate for 5, 6, 7, 8, 9, and 10 training sets were 94.444%, 97.333%, 98.333%, 100%, 100% and 100% respectively. Based on Table 4, the maximum recognition rate increased proportionally to the number of training sets used. The more number of training set used, the faster maximum recognition rate is reached [Arif et

The experimental results of the 1st, 2nd, and 3rd scenarios were compared to other methods, such as PCA, LDA/QR, and LPP/QR as seen in Table 5, whereas for the 4th and 5th scenarios were not compared, since they have achieved maximum result (100%). The recognition rate of 5, 6, and 7 training set, for both on the ORL and the YALE face database, "The Maximum Value Selection of Kernel Principal Component Analysis", outperformed the other methods.


Table 4. The YALE Face Database Recognition Rate using Maximum Feature Value Selection Method of Non linear Function based on KPCA


