Abstract Face recognition is considered to be one of the most reliable biometric, when security issues are taken into concern. For this, feature extraction becomes a critical problem. Different methods are used for extraction of facial feature which are broadly classified into linear and nonlinear subspaces. Among the linear methods are Linear Discriminant Analysis (LDA), Bayesian Methods (MAP and ML), Discriminative Common Vectors (DCV), Independent Component Analysis (ICA), Tensor faces Multi-Linear Singular Value Decomposition (SVD), Two Dimensional PCA (2DPCA), Two Dimensional LDA (2D-LDA) etc., but Principal Component Analysis (PCA) is considered to be one the classic method in this field. Based on this a brief comparison of PCA family is drawn, of which PCA, Kernel PCA (KPCA), 2DPCA and Two Dimensional Kernel (2DKPCA) are of major concern. Based on literature review recognition performance of PCA family is analyzed using the databases named YALE, YALE-B, ORL and CMU. Concluding remarks about testing criteria set by different authors as listed in literature reveals that K series of PCA produced better results as compared to simple PCA and 2DPCA on the aforementioned datasets.

References

[1] Belhumeur N., Hespanha P., and Kriegman J., Eigenfaces vs. Fisherfaces: Recognition using Class Specific Linear Projection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, 1997.

[2] Cevikalp H., Neamtu M., Wilkes M., and Barkana A., Discriminative Common Vectors for Face Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 1, pp. 4-13, 2005. A Survey: Linear and Nonlinear PCA Based Face Recognition Techniques 543

[3] Chen S., Shan T., and Lovell C., Robust Face Recognition in Rotated Eigenspaces, in Proceedings of Image and Vision Computing New Zealand, New Zealand, pp. 1-6, 2007.

[4] Chen S., Sun Y., and Yin B., A Novel Hybrid Approach Based on Sub-Pattern Technique and Extended 2DPCA for Color Face Recognition, in Proceedings of the 11 th IEEE International Symposium on Multimedia, China, pp. 630-634, 2009.

[5] Cong-De L., Yu-Lei C., and Bin-Bin H., Kernel Based 2D Symmetrical Principal Component Analysis for Face Classification, in Proceedings of the 7 th International Conference on Machine Learning and Cybernetics, Kunming, vol. 1, pp. 442-447, 2008.

[6] Epstein R., Hallinan P., and Yuille A., 5 2 Eigenimages Suffice: An Empirical Investigation of Low-Dimensional Lighting Models, in Proceedings of the Workshop on Physics Based Modeling in Computer Vision, Cambridge, pp. 108-116, 1995.

[7] Graham F., Dueck J., Funt B., and Drew M., Color Eigenfaces, in Proceedings of IEEE 3 rd International Workshop on Image and Signal Processing Advances in Computational Intelligence, UK, pp. 607-610, 1996.

[8] Fukunaga K., Introduction to Statistical Pattern Recognition, Academic Press Professional, USA, 1990.

[9] Gottumukkal R. and Asari K., An Improved Face Recognition Technique Based on Modular PCA Approach, Pattern Recognition Letters, vol. 25, no. 4, pp. 429-436, 2004.

[10] Gross R., Matthews I., and Baker S., Eigen Light-Fields and Face Recognition Across Pose, in Proceedings of the 5 th IEEE International Conference on Automatic Face and Gesture Recognition, Washington, pp. 1-7, 2002.

[11] Hallinan W., A Low-Dimensional Representation of Human Faces for Arbitrary Lighting Conditions, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, pp. 995- 999, 1994.

[12] He X., Yan S., Hu Y., Niyogi P., and Zhang H., Face Recognition using Laplacianfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 3, pp. 328-340, 2005.

[13] Hjelmas E. and Wroldsen J., Recognizing Faces from the Eyes Only, in Proceedings of the 11 th Scandinavian Conference on Image Analysis, pp. 1-5, 1999.

[14] Jaam J., Rebaiaia M., and Hasnah A., A Fingerprint Minutiae Recognition System Based on Genetic Algorithms, International Arab Journal Information Technology, vol. 3, no. 3, pp. 242-248, 2006.

[15] Kirby M. and Sirovich L., Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 103-108, 1990.

[16] Kong H., Li X., Wang L., Teoh E., Wang J., and Venkateswarlu R., Generalized 2D Principal Component Analysis, in Proceedings of International Joint Conference on Neural Networks, Canada, vol. 1, pp. 108-113, 2005.

[17] Kong H., Wang L., Teoh K., Li X., Wang J., and Venkateswarlu R., Generalized 2D Principal Component Analysis for Face Image Representation and Recognition, Neural Networks, vol. 18, no. 5-6, pp. 585-594, 2005.

[18] Li J., Zhao B., and Zhang H., Face Recognition Based on PCA and LDA Combination Feature Extraction, in Proceedings of the 1 st International Conference on Information Science and Engineering, Nanjing, pp. 1240-1243, 2009.

[19] Liang Y., Lai J., Zou Y., Zheng W., and Yuen P., Face Hallucination Through Kpca, in Proceedings of the 2 nd International Congress on Image and Signal Processing, Tianjin, pp. 1-5, 2009.

[20] Liu C., Gabor-Based Kernel PCA with Fractional Power Polynomial Models for Face Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 572-581, 2004.

[21] Liu N., Wang H., and Yau W., Face Recognition with Weighted Kernel Principal Component Analysis, in Proceedings of the 9 th International Conference on Control, Automation, Robotics and Vision, Singapore, pp. 1-5, 2006.

[22] Lu C., Zhang C., Zhang T., and Zhang W., Kernel Based Symmetrical Principal Component Analysis for Face Classification, Neurocomputing, vol. 70, no. 4-6, pp. 904-911, 2007.

[23] Lu J., Plataniotis N., and Venetsanopoulos N., Face Recognition using Kernel Direct Discriminant Analysis Algorithms, IEEE Transactions on Neural Networks, vol. 14, no. 1, pp. 117-126, 2003.

[24] Matthew T., A Random Walk Through Eigenspace, IEICE Transactions on Information and Systems, vol. 84, no. 12, pp. 1586-1595, 2001.

[25] Moon H. and Phillips J., Computational and Performance Aspects of PCA-Based Face- Recognition Algorithms, Perception, vol. 30, no. 3, pp. 303-322, 2001.

[26] Murase H. and Nayar K., Visual Learning and Recognition of 3-D Objects from Appearance, International Journal of Computer Vision, vol. 14, no. 1, pp. 5-24, 1995. 544 The International Arab Journal of Information Technology, Vol. 10, No. 6, November 2013

[27] Murtaza M., Sharif M., Raza M., and Shah J., Face Recognition using Adaptive Margin Fisher s Criterion and Linear Discriminant Analysis, International Arab Journal of Information Technology, vol. 11, no. 2, pp. 1-11, 2014.

[28] Nayar K., Nene A., and Murase H., Subspace Methods for Robot Vision, IEEE Transactions on Robotics and Automation, vol. 12, no. 5, pp. 750-758, 1996.

[29] Nhat V. and Lee S., Improvement on PCA and 2DPCA Algorithms for Face Recognition, in Proceedings of Lecture Notes in Computer Science, Berlin , pp. 568-577, 2005.

[30] Nhat V. and Lee S., Kernel-Based 2DPCA for Face Recognition, in Proceedings of IEEE International Symposium on Signal Processing and Information Technology, Gaza, pp. 35-39, 2007.

[31] Nicholl P. and Amira A., DWT/PCA Face Recognition using Automatic Coefficient Selection, in Proceedings of the 4 th IEEE International Symposium on Electronic Design, Test and Applications, Hong Kong, pp. 390-393, 2008.

[32] Pang Y., Tao D., Yuan Y., and Li X., Binary Two-Dimensional PCA, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 38, no. 4, pp. 1176-1180, 2008.

[33] Pentland A., Moghaddam B., and Starner T., View-Based and Modular Eigenspaces for Face Recognition, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, pp. 84-91, 1994.

[34] Pereira J., Cavalcanti G., and Ren T., Modular Image Principal Component Analysis for Face Recognition, in Proceedings of International Joint Conference on Neural Networks, USA, pp. 2481-2486, 2009.

[35] Poon B., Amin M., and Yan H., PCA Based Face Recognition and Testing Criteria, in Proceedings of the 8 th International Conference on Machine Learning and Cybernetics, Baoding, vol. 5, pp. 2945-2949, 2009.

[36] Qader H., Ramli R., and Al-Haddad S., Fingerprint Recognition using Zernike Moments, International Arab Journal of Information Technology, vol. 4, no. 4, pp. 372- 376, 2007.

[37] Sch lkopf B., Smola A., and M ller K., Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, vol. 10, no. 5, pp. 1299-1319, 1998.

[38] Sharif M., Javed M., and Mohsin S., Face Recognition Based on Facial Features, Research Journal of Applied Sciences, Engineering and Technology, vol. 4, no. 17, pp. 2879-2886, 2012.

[39] Sharif M., Mohsin S., Jamal M., and Raza M., Illumination Normalization Preprocessing for Face Recognition, in Proceedings of the 2 nd Conference on Environmental Science and Information Application Technology, Wuhan, vol. 2, pp. 44-47, 2010.

[40] Sharif M., Mohsin S., and Javed M., Real Time Face Detection using Skin Detection (Block Approach), Journal of Applied Computer Science and Mathematics, vol. 5, no. 10, pp. 75- 81, 2011.

[41] Sharif M., Mohsin S., Javed M., and Ali M., Single Image Face Recognition using Laplacian of Gaussian and Discrete Cosine Transforms, International Arab Journal of Information Technology, vol. 9, no. 6, pp. 562-570, 2012.

[42] Shashua A., Geometry and Photometry in 3D Visual Recognition, PhD Thesis, Massachusetts Institute of Technology Cambridge, USA, 1992.

[43] Sirovich L. and Kirby M., Low-Dimensional Procedure for the Characterization of Human Faces, Jorurnal of Optical Society of America, vol. 4, no. 3, pp. 519-524, 1987.

[44] Hongta S., Feng D., and Zhao R., Face Recognition using Multi-Feature and Radial Basis Function Network, in Proceedings of the Pan-Sydney Area Workshop on Visual Information Processing, Sydney, pp. 183-189, 2002.

[45] Sun Z., Yang W., Sun C., and Shen J., Face Recognition using DT-CWT Feature-Based 2DPCA, in Proceedings of Chinese Conference on Pattern Recognition, Chongqing, pp. 1-5, 2010.

[46] Swets L. and Weng J., Using Discriminant Eigenfeatures for Image Retrieval, IEEE Transactions on Pattern Analysi s and Machine Intelligence, vol. 18, no. 8, pp. 831-836, 1996.

[47] Tang F., Crabb R., and Tao H., Representing Images using Nonorthogonal Haar-Like Bases, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 12, pp. 2120- 2134, 2007.

[48] Tao H., Rui L., and Mei-Juan Z., Face Recognition under Complex Conditions, in Proceedings of International Conference on Electrical and Control Engineering, Wuhan, pp. 960-963, 2010.

[49] Turk M. and Pentland A., Eigenfaces for Recognition, Journal of Cognitive Neuroscience, vol. 3, no. 1, pp. 71-86, 1991.

[50] Wang L., Wang X., and Feng J., On Image Matrix Based Feature Extraction Algorithms, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 36, no. 1, pp. 194-197, 2006.

[51] Wang X., Huang C., Fang X., and Liu J., 2DPCA vs. 2DLDA: Face Recognition using A Survey: Linear and Nonlinear PCA Based Face Recognition Techniques 545 Two-Dimensional Method, in Proceedings of International Conference on Artificial Intelligence and Computational Intelligence, Shanghai, vol. 2, pp. 357-360, 2009.

[52] Wang Y. and Zhang Y., Facial Recognition Based on Kernel PCA, in Proceedings of the 3 rd International Conference on Intelligent Networks and Intelligent Systems, Shenyang, pp. 88-91, 2010.

[53] Wang Z. and Li X., Face Recognition Based on Improved PCA Reconstruction, in Proceedings of the 8 th World Congress on Intelligent Control and Automation, Jinan, pp. 6272-6276, 2010.

[54] Wei X., Sheng Y., Qi W., and Ming L., Face Recognition Based on Wavelet Transform and PCA, in Proceedings of Pacific-Asia Conference on Knowledge Engineering and Software Engineering, Shenzhen, pp. 136-138, 2009.

[55] Xiao-Jie W., Modular PCA Based on Within- Class Median for Face Recognition, in Proceedings of the 3 rd IEEE International Conference on Computer Science and Information Technology, Chengdu, vol. 1, pp. 52- 56, 2010.

[56] Xu A., Jin X., Jiang Y., and Guo P., Complete Two-Dimensional PCA for Face Recognition, in Proceedings of the 18 th International Conference on Pattern Recognition, Hong Kong, vol. 3, pp. 481-484, 2006.

[57] Yang J., Zhang D., Frangi F., and Yang J., Two- Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 131-137, 2004.

[58] Yang M., Kernel Eigenfaces vs. Kernel Fisherfaces: Face Recognition using Kernel Methods, in Proceedings of the 5 th IEEE International Conference on Automtic Face and Gesture Recognition, USA, pp. 215-220, 2002.

[59] Zhang D., Zhou Z., and Chen S., Diagonal Principal Component Analysis for Face Recognition, Pattern Recognition, vol. 39, no. 1, pp. 140-142, 2006.

[60] Zhang J., Fei X., and Zhang Y., A New Method for Face Recognition Based on PCA Optimize Strategy, in Proceedings of International Conference on Computer Application and System Modeling, Taiyuan, vol. 10, pp. 417-420, 2010.

[61] Zhao W., Discriminant Component Analysis for Face Recognition, in Proceedings of the 15 th International Conference on Pattern Recognition, Barcelona, vol. 2, pp. 818-821, 2000.

[62] Zheng W., Lai H., and Li Z., 1D-LDA vs. 2D- LDA: When is Vector-Based Linear Discriminant Analysis Better Than Matrix-Based?, Pattern Recognition, vol. 41, no. 7, pp. 2156-2172, 2008. Jamal Hussain Shah is Lecturer in Computer Science Department at COMSATS Institute of Information Technology, Pakistan. His research areas are digital image processing and networking. He are include has more than 3 years experience in IT- related projects, he developed and designed ERP systems for different organizations of Pakistan. Muhammad Sharif has been an assistant professor at Department of Computer Science, COMSATS Institute of Information Technology Pakistan. He is also PhD Scholar at COMSATS Institute of Information Technology. He has more than 17 years of experience including teaching graduate and undergraduate classes. Mudassar Raza is an assistant professor at COMSATS Institute of Information Technology, Pakistan. He has more than seven years of experience of teaching undergraduate classes at CIIT Wah. He has been supervising final year projects to undergraduate students. His interest include are digital image processing, and parallel and distributed computing. Aisha Azeem is a Lecturer in University of Wah, Pakistan. She completed her BS and MS degrees from CIIT Wah in 2008 and 2011 respectively. Her research interests include digital image processing and software engineering.