近年來，利用生物特徵中的人臉辨識已經成為一項熱門的研究領域。人臉辨識之所以會受到歡迎是因為比起其他的生物辨識像是指紋、掌紋、虹膜等，它具有較少的侵入性容易被大眾所接受。
雖然已經有非常多關於人臉辨識的論文，但是我們比較喜歡使用基於投影向量的人臉辨識，因為這種方法不僅可以用來重建人臉的圖像，還可以把人臉圖像的特徵持萃取出來。除此之外，基於投影向量的人臉辨識方法擁有比使用其他方法相較高的辨識率。
在本論文中，我們藉由論文所提供的演算法，試著研究且實做出五種基於投影向量的人臉辨識方法，並且達到論文所提及的結果。我們研究的五種分別是 Eigenface、Fisherface、2DPCA、2DLDA和SVD，這些方法都是在基於投影向量的人臉辨識上非常重要的論文。
我們的實驗是使用 k-nearest neighbor分類法來分類，使用不同的k值（k值為1到10）實做在AT&T, UMIST 和 NTHU 人臉資料庫上，辨識率將在往後論文中提及，這些方法中SVD這個方法在我們的環境下表現似乎優於其他方法。

References

[AT&T] AT&T Laboratories Cambridge – The Database of Faces
(http://www.cl.cam.ac.uk/Research/DTG/attarchive/facedatabase.html)

[Belh1997] P.N. Belhumeur, J.P. Hespanha, and D.J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition Using class specific linear projection”, IEEE Transaction on Pattern Analysis and Machine Intelligence, Special Issue on Face Recognition, Vol. 15, No. 7, 1997.

[Bach2002] F.R. Bach and M.I. Jordan, “Kernel Independent Component Analysis”, Journal of Machine Learning Research, 3, 1-48, 2002.

[Bart2002] M.Bartlett and T. Sejnowski, “Face Recognition by Independent Component Analysis”, IEEE Trans. On Neural Networks, Vol. 13, No. 6, 1159-1450, 2002.

[Cho2006] D.U. Cho, U.D. Chang, K.D. Kim, B.H. Kim, and S.H. Lee, ”(2D)2 DLDA for Efficient Face Recognition”, First Pacific Rim Symposium, PSIVT 2006, LNCS 4319, 314-321, 2006.

[Dagh2006] I. Dagher and R. Nachar, ”Face Recognition Using IPCA-ICA Algorithm”, IEEE Trans.on Pattern Analysis and Machine Intelligence, Vol. 28, No. 6, 996-1000, 2006.

[Daug2004] J. Daugman, “How Iris Recognition works”, IEEE Trans. on Circuits and Systems for Video Technology, Vol. 14, No. 1, 21-30, 2004.

[Duda2001] R.O. Duda, P.E. Hart, and D.G. Stork, “Pattern Classification”, Wiley, 2nd edition, 2001.

[Fuku1990] K. Fukunaga, “Introduction to Statistical Pattern Recognition”, Academic Press, 2nd edition, 1990.

[Horn1985] R. Horn and C. Johnson, “Matrix Analysis”, Cambridge University Press, 1985.

[Hsu2006] C.H. Hsu, “New Projection-based Features for Face Recognition”, Master Thesis, National Tsing Hua University, Taiwan, March, 2006
.
[Joll1986] I.T. Jolliffe, “Principal Component Analysis”, Springer-Verlag, 1986.

[Karh1997] J. Karhunen, “A Class of Neural Networks for Independent Component Analysis”, IEEE Trans. on Neural Networks, Vol. 8, No. 3, 486-504, 1997.

[Li2005] M. Li and B. Yuan, “2D-LDA: A statistical linear discriminant analysis for image matrix”, Pattern recognition Letters, Vol. 26, No. 5, 527-532, 2005.

[Mika1999] S. Mika, G. Ratsch, J.Weston, B. Scholkopf, and K.R. Muller, “Fisher Discriminant Analysis with Kernels”, IEEE International Workshop on Neural Networks for Signal Processing, Vol. 9, 41-48, 1999.

[Malt2005] D. Maltoni, D. Maio, A. Jain, and S. Prabhakar, “Handbook of Fingerprint Recognition”, Springer, 2005.

[Phil2000] P.J. Phillils, H. Moon, S.A. Rizvi, and P.J. Rauss, ”The FERET Evaluation Methodology for Face Recognition Face-Recognition Algorithms”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 22, No. 10, 1090-1104, 2000.

[Sam1994] F.S. Samaria and A.C. Harter, “Parameterisation of a Stochastic Model for Human Face Identification”, Proceedings of 2nd IEEE Workshop on
Applications of Computer Vision, Sarasota (Florida), 1-5, 1994.

[Swee1996] D.L. Sweets and J. Weng, “Using Discriminant Eigenfeatures for Image Retrieval”, IEEE Trans. on PAMI, Vol. 18, No. 8, 831-836, 1996.

[Theo2006] S. Theodoridis and K. Koutroumbas, “PATTERN RECOGNITION”, Academic Press, 3rd edition, 2006.

[Turk1991] M. Turk and A. Pentland, “Eigenfaces for Recognition”, Journal of Cognitive Neuroscience, Vol. 3, No. 1,71-86, 1991.

[Web01] http://www.cs.nthu.edu.tw/~cchen/

[Web02] http://images.ee.umist.ac.uk/danny/database.html

[Yang2000] M.H. Yang, N. Ahuja, and D. Kriegman, “Face recognition kernel eigenfaces”, Image Processing, Vol. 1, 37-40, 2000.

[Yang2002] M.H. Yang, “Kernel Eigenfaces vs. Kernel Fisherfaces: Face Recognition Using Kernel Methods”, IEEE Trans. on Automatic Face and Gesture, 215, 2002.

[Yang2004] J. Yang and 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, 131-137, 2004.

[Yang2005] J. Yang, D. Zhang, Z. Jin, and J.Y. Yang, “Two-dimensional discriminant trainsform for face recognition”, Pattern recognition, Vol. 38, Issue 7, 1125-1129, 2005.

[Yang2006] J. Yang, D. Zhang, Z. Jin, and J.Y. Yang, “Unsupervised Discriminant Projection Analysis for Feature Extraction”, Proceeding of International Conference on Pattern Recognition, Vol. 1, August 14-16, Hong Kong, China, 2006.

[Zhao1999] W. Zhao, R. Chellappa, and P.J. Phillips, “Subspace Linear Discriminant Analysis for Face Recognition”, Technical Report CAR-TR-914, Center for Automation Research, University of Maryland, 1999.

[Zhao2003] W. Zhao, R. Chellappa, P.J. Phillips, and J. Rosenfeld, “Face Recognition: Literature Survey”, ACM computing surveys”, Vol. 35, No.4, 399-458, 2003.