3. Experiments and analysis 1 The ORL database
3.2 Experiments and analysis of SI2DPCA
According to Table 1, the computation cost of SI2DPCA and 2DPCA can be calculated for the images in ORL database. Every image has dimension of 112×92, meaning m and n in Table 1 are 112 and 92 respectively. And each image is divided into 4 smaller sub-images, meaning the value of k in Table 1 is 4. Suppose 200 images are taken as training data, meaning N in Table 1 is 200, and 8 features are selected and extracted. Putting these values into Table 1, the result is shown in Table 3.
Table 3 shows that the computation cost for SI2DPCA is only half of 2DPCA. When calculating covariance matrix and eigen-decomposition, there are many quadratic or cubic power computations.
Smaller image dimensions operated in SI2DPCA can greatly reduce the computation cost, as discussed previously
Table 3: Analysis of computation cost for ORL database
Computation type 2DPCA SI2DPCA
9
Data average computation
200×(112×92)+1
=2060801
4×200×(56×46) +4=2060804 Covariance matrix
computation
200×(2×112×92 + 923+112×92)+1
= 161920001
4×200×(2×56×46 +463+56×46)+4
=84051204 Eigen-
decomposition computation
4×1122×92 + 8×112×922 + 9×923
=19208128
4×(4×562×46+8×56
×462+9×463)
= 9604064 Sum of
computation cost 183188930 95716072
Besides the computation cost, the proposed SI2DPCA and conventional 2DPCA also need be compared on their recognition performance. The recognition is performed by the nearest neighbor rule (NNR) [11] that is based on Euclidean distance.
In this experiment, the first 5 images of every face are treated as training and the remained 5 images of every face are treated as testing images. That is, there are 200 images for training and 200 images for testing. Eight important features are extracted in the experiment, meaning a 8-elements feature vector is obtained for each of images. The projected feature vector of each of training and testing images can be calculated by multiplying the 8-elements feature vectors to the data of every training and testing images. The classification for each of testing images can then be performed by NNR against the training images.
The recognition rate comparison between 2DPCA and SI2DPCA is shown in Table 4. Earlier discussions argued that important features can be better recognized and extracted in smaller sub-images. This can be observed in Table 4 that shows slight better recognition rate for SI2DPCA over conventional 2DPCA. Both Table 3 and Table 4 together show that the SI2DPCA reduces computation cost without compromising its recognition performance.
Table 4: Recognition comparison between 2DPCA and SI2DPCA Strategy Recognition rate
2DPCA 93%
SI2DPCA 93.5%
Various methodologies based on 2DPCA have been proposed. Table 5 shows the performance comparison in terms of recognition rate and computation cost among some of better-known approaches and SI2DPCA. All the experiments for the approaches in Table 5 are conducted based on the face images in ORL database. In Table 5, the computation costs of method 1, method 2 and method 3 are all higher than SI2DPCA while the recognition rates are either lower than or same as
10
SI2DPCA. This is because SI2DPCA operates against matrices in smaller dimensions. For methods (4), (5) and (6) in Table 5, they even put additional processes to 2DPCA. Method 5 combines 2DPCA with Kernel algorithm. This approach projects image data to high dimensional space, causing high computation cost. Although its recognition rate is slightly better than the proposed SI2DPCA, the much higher computation cost makes it difficult for practical applications. Method 6 combines feature fusion with 2DPCA in order to increase recognition rate. The resultant recognition rate is very good at 98.1% that is better than the rate of 93.5% by SI2DPCA in the experiment. Unfortunately, the computation cost of this approach is so high, at least 10 times higher than 2DPCA, that it is impossible to be applied to any practical applications.
Table 5: Comparison among other methods and SI2DPCA Metho
d number
Method Recognitio n rate
Computation cost
1 (2D)2PCA [12] 90.5% high
2 2DPCA+Fusion method based on bidirectional [17]
92.5% high
3 2DPCA+2DLDA [14] 93.5% high
4
SI2DPCA (proposed) 93.5% low
5 2DPCA+Kernel [22] 94.58% very high
6 2DPCA+Feature fusion approach [23] 98.1% very very high
4. Conclusion
The feature extraction algorithm 2DPCA is specially developed for face recognition. Its characteristics are low computation cost and good feature extraction, making 2DPCA a popular approach for face recognition. In this paper, an enhanced approach “SI2DPCA” is proposed to operate at even lower computation cost without compromising its good recognition performance. Both of the two goals of reducing computation cost and maintaining good recognition rate have been shown in the results of the conducted experiments in this paper.
References
[1] A. Z. Kouzani, F. He, and K. Sammut, “Towards invariant face recognition,” Inf. Sci., vol. 123, pp.
75–101, 2000.
[2] M. J. Er, S. Wu, J. Lu, and H. L. Toh, “Face recognition with radial basis function RBF neural networks,” IEEE Trans. Neural Netw., vol. 13, no. 3, pp. 697–710, May 2002.
[3] F. Yang and M. Paindavoine, “Implementation of an RBF neural network on embedded systems:
11
Real-time face tracking and identity verification,” IEEE Trans. Neural Netw., vol. 14, no. 5, pp.
1162–1175, Sep. 2003.
[4] J. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, “Face recognition using kernel direct discriminant analysis algorithms,” IEEE Trans. Neural Netw., vol. 14, no. 1, pp. 117–126, Jan. 2003.
[5] B. K. Gunturk, A. U. Batur, and Y. Altunbasak, “Eigenface-domain super-resolution for face recognition,” IEEE Trans. Image Process., vol. 12, no. 5, pp. 597–606, May 2003.
[6] B. L. Zhang, H. Zhang, and S. S. Ge, “Face recognition by applying wavelet subband representation and kernel associative memory,” IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 166–177, Jan. 2004.
[7] Q. Liu, X. Tang, H. Lu, and S. Ma, “Face recognition using kernel scatter-difference-based discriminant analysis,” IEEE Trans. Neural Netw., vol. 17, no. 4, pp. 1081–1085, Jul. 2006.
[8] W. Zheng, X. Zhou, C. Zou, and L. Zhao, “Facial expression recognition using kernel canonical correlation analysis (KCCA),” IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 233–238, Jan. 2006.
[9] X. Tan, S. Chen, Z. H. Zhou, and F. Zhang, “Recognizing partially occluded, expression variant faces from single training image per person with SOM and soft k-NN ensemble,” IEEE Trans. Neural
Netw., vol. 16, no. 4, pp. 875–886, Jul. 2005.
[10] G. Huang, “Fusion (2D)2PCALDA: A new method for face recognition,” Applied Mathematics
and Computation, 216, pp. 3195–3199, 2010.
[11] J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition,” IEEE Trans. Pattern Analysis and Machine
Intelligence., vol. 26, no. 1, pp. 131-137, Jan. 2004.
[12] D. Zhang and Z. H. Zhoua, “(2D)^2PCA: Two-directional two-dimensional PCA for efficient face representation and recognition,” Neurocomputing 69, pp. 224–231, Jun. 2005.
[13] W. H. Yang and D. Q. Dai, “Two-Dimensional Maximum Margin Feature Extraction for Face Recognition,” IEEE Transactions on Systems, Man and Cybernetics., vol. 39, no. 4, pp. 1002-1012, Aug, 2009.
[14] P. Sanguansat, W. Asdornwised, S. Jitapunkul and S. Marukatat, “Tow-dimensional linear discriminant analysis of principle component vectors for face recognition,” IEEE., pp. 345-348, 2006.
[15] J. Meng and W. Zhang, “Volume measure in 2DPCA-based face recognition,” Pattern
Recognition Letters 28, pp. 1203–1208, Jan. 2007.
[16] H. Wang, S. Chen, Z. Hu and B. Luo, “Probabilistic two-dimensional principal component analysis and its mixture model for face recognition,” Springer Neural Comput & Applic 17, pp.
541–547, 2008.
[17] Y. G. Kim, Y. J. Song, U. D. Chang, D. W. Kim, T. S. Yun and J. H. Ahn, “Face recognition using a fusion method based on bidirectional 2DPCA,” Applied Mathematics and Computation., vol.
12
205, pp. 601–607, 2008.
[18] Y. Qi and J. Zhang, “(2D)2PCALDA: An efficient approach for face recognition,” Applied
Mathematics and Computation., vol. 213(1), pp. 1-7, Jul. 2009.
[19] S. J. Leon, Linear algebra with applications, seventh ed. Prentice Hall, 2006.
[20] 3D Computer Vision Winter Term 2005/06, Nassir Navab
[21]“The ORL face database”, http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.htm [22] N. Sun, H. X. Wang, Z. H. Ji, C. R. Zou and L. Zhao, “An efficient algorithm for Kernel two-dimensional principal component analysis,” Neural Comput & Applic., 17, pp. 59-64, 2008.
[23] Y. Xu, D. Zhang, J. Yang and J. Y. Yang, “An approach for directly extracting features from matrix data and its application in face recognition,” Neurocomputing, 71, pp. 1857-1865, Feb, 2008.
13
Conference on Artificial Intelligence (ICAI 2012) - decision on your paper (ICA2902)
Thursday, April 26, 2012 7:45 AM
From:
"Steering Committee" <sc@world-comp.org>
Add sender to Contacts
To:
yingkyang@yahoo.com
Cc:
yingkyang@yahoo.com
Dear Dr. Yingkuei Yang:
I am pleased to inform you that the following paper which you submitted to:
The 14th International Conference on Artificial Intelligence
(ICAI'12: July 16-19, 2012, USA) has been accepted as a Regular Research Paper (RRP) - ie, accepted for both, publication in the proceedings and oral formal presentation. Please see below for the categories of accepted papers.
Paper ID #: ICA2902
Title: A Fuzzy-Reasoning Radial Basis Function Neural Network with Reinforcement Learning Method
Author(s): Ying-Kuei Yang, Jin-Yu Lin, Wei-Li Fang and Jung-Kuei Pan
Note: The "paper ID #" shown above is composed of three letters
(conference prefix) followed by four numeral/digits. You will need to have this "Paper ID #" at the time of registration and final paper submission (for publication).
14