occlu-4.5. CROSS VALIDATION
training set testing set
N F3 L3 G1 S1
F1, F2 81.66 75.51 33.73 43.91 68.7712 L1, L2 33.10 32.66 41.28 24.40 30.5225 G2, G3 27.82 27.49 27.64 28.87 16.3963 S2, S3 49.14 35.44 59.90 48.33 64.7425
Table 4.9: Cross validation result. There are four kinds of training set: smile
& anger facial expression (F1, F2), left & right lights (L1, L2), sunglasses occlusion with left & right light (G2, G3) and scarf occlusion with left &
right light (S2, S3). On the other hand, six kinds of testing set are used for experiment: neutral facial expression (N), scream facial expression (F3), both lights (L3), sunglasses occlusion (G1) and scarf occlusion (S1).
Figure 4.14: Total Success Rate (TSR) of each testing set under four kinds of training set.
4.5. CROSS VALIDATION
sion and illumination variation, almost every testing set produces the lowest recognition rate compared to its corresponding ones under different train-ing sets. As we expect, the recognition rate of facial images with sunglasses occlusion is the highest and slightly higher than the others. Therefore, we conclude that eyes are essential facial features for face recognition. When the training set consists of facial images with sunglasses occlusion and the testing set consists of facial images with scarf occlusion, the lowest recogni-tion rate occurs. It indicates that the most two significant facial features in face recognition are eyes and mouth.
Given facial images with scarf occlusion and illumination variation as training set, facial images with sunglasses occlusion produces the highest to-tal success rate. Due to the close relation between the training set and testing set, the experimental result is expectable. Note that, in this case, the lowest total success rate occurs when using scream facial images as testing set. The reason is that the critical feature in the scream facial image is its mouth which is occluded in the training images. When neutral images are trained during the feature extraction as shown before, the wBNMF method withstands well for facial images under various conditions. Moreover, this experiment is used to measure the recognition performance when large variations are introduced to the training images.
Chapter 5 Conclusion
In this paper, we proposed a novel image representation approach, called basis-emphasized non-negative matrix factorization with wavelet transform (wBNMF), which is applied for face recognition. The proposed approach is a parts-based algorithm that not only keeps the non-negative constraint on basis and coefficients, but also enhances the intuitive parts of basis images with respect to the original NMF by adding the orthonormal characteristic taken from PCA approach. Furthermore, we incorporated wavelet transform (WT) with the BNMF decomposition in order to reduce undesired noise disturbance. We solved the new optimization by developing update rules for both the weighting coefficients and the bases.
To further analyze, we explored the advantages of PCA and NMF for
extracting intuitive facial features. Unlike previous non-negative matrix fac-torization (NMF), the novel algorithm studied in this paper is very effective in face recognition. Since the traditional Euclidean metric does not take into account the positive aspects of NMF, different distance metrics, such as L1, correlation, cosine angle, Mahalanobis and Riemannian, have been tested with the learned wBNMF positive projected vectors. As a result, we find that the Riemannian metric is the most suitable distance metric among all the others. Moreover, the recognition accuracy using the Riemannian metric is better than that using the classical combination of PCA and the Euclidean distance.
We have experimentally demonstrated the advantages of wBNMF using three well-known databases, the CBCL, ORL and AR face database. The images subjected to strong illumination variation and different facial expres-sions were used in the experiments to establish the robustness of face recog-nition. But the overall performance of the illumination variation test was insignificant when compared with the results for the large facial expression change indicating the sensitivity of the wBNMF approach to lighting varia-tions. In addition, the most striking aspect of the algorithm is that wBNMF has a good response under the presence of occlusion because it is based on a basis-emphasized local representation in front of the PCA global one. Thus, when occlusion is present, wBNMF combined with the Riemannian metric improves other techniques. For this reason, we believe that wBNMF can be a relevant technique for pattern recognition problems, where occlusion that can not be handled by PCA may appear.
face recognition. Invariably, these algorithms aim to factorize the original data into basis vectors and corresponding coefficients. The difficulty is how to make sure of learning meaningful basis vectors so that the computed lin-ear structures are close to the real one. In our case, the linlin-ear structures are hidden among the input image, and the task is to detect them for face recognition. As far as the image representation is concerned, wBNMF is a good trade-off between local image representation produced by NMF and the holistic image representation produced by PCA. Finally, we applied the new decomposition to frontal face verification where better performance than PCA and NMF has been achieved.
BIBLIOGRAPHY
Bibliography
[1] MIT Center for Biological and Computation Learning, “The CBCL face database,” Available at: http://cbcl.mit.edu/cbcl/software-datasets/FaceData2.html
[2] AT&T Laboratories, Cambridge, U.K., “The ORL face database,”
Available at: http://www.orl.co.uk/facedatabase.html
[3] A. M. Martinez and R. Benavente, “The AR face database,” Techni-cal Report 24, Computer Vision Center (CVC), Barcelona, Spain, June 1998.
[4] M. A. Turk and A. P. Pentland, “Face recognition using eigenfaces,” Pro-ceedings of IEEE Conference on Computer Vision and Pattern Recogni-tion (CVPR), pp. 586–591, Hawaii, June 1991.
BIBLIOGRAPHY
[5] L. Sirovich and M. Kirby, “Low-dimensional procedure for the charac-terization of human faces,” Journal of the Optical Society of America, vol. 4, no. 3, pp. 519–524, March 1987.
[6] M. Kirby and L. Sirovich, “Application of the Karhunen-Loeve proce-dure for the characterization of human faces,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 103–108, January 1990.
[7] D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature, vol. 401, pp. 788–791, 1999.
[8] D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” Advances in Neutral Information Processing 13 (Proc.
NIPS*2000), MIP Press, 2001.
[9] D. Guillamet and J. Vitri`a, “Unsupervised learning of part-based rep-resentation,” Computer Analysis of Images and Patterns, W. Skarbek (Eds.) Lecture Notes in Computer Science 2124, Springer, pp. 700–708, 2001.
[10] M. Juvela, K. Lehtinen, and P. Paatero, “The use of positive matrix fac-torization in the analysis of molecular line spectra from the thumbprint nebula,” In D. P. Clemens and R. Barvainis, editors, Clouds, Cores, and Low Mass Stars, ASP Conference Series, vol. 65, pp. 176–180, 1994.
[11] M. Juvela, K. Lehtinen, and P. Paatero, “The use of positive matrix fac-torization in the analysis of molecular line spectra,” MNRAS, vol. 280,
BIBLIOGRAPHY
[12] P. Comon, “Independent component analysis – a new concept?,” Signal Procesing, vol. 36, pp. 287–314, 1994.
[13] Hyv¨arinen, J. Karhunen, and E. Oja, “Independent Component Analy-sis,” Wiley Interscience, 2001.
[14] S. Z. Li, X. Hou, H. Zhang, and Q. Cheng, “Learning spatially local-ized parts-based representations,” Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. I, pp. 207–212, Hawaii, USA, 2001.
[15] D. Guillamet and J. Vitri`a, “Evaluation of distance metrics for recog-nition based on non-negative matrix factorization,” Pattern Recogrecog-nition Letters, vol. 24, pp. 1599–1605, June 2003.
[16] D. Guillamet and J. Vitri`a, “Determining a suitable metric when using non-negative matrix factorization,” Proceedings of the 16th International Conference on Pattern Recognition (ICPR 2002), pp. 128–131, Quebec, 2002.
[17] W. Liu and N. Zheng, “Non-negative matrix factorization based meth-ods for object recognition,” Pattern Recognition Letters, vol. 25, no. 8, pp. 893–897, June, 2004.
[18] P. O. Hoyer, “Non-negative sparse coding,” Neural Networks for Signal Processing XII (Proc. IEEE Workshop on Neural Networks for Signal Processing), pp. 895–898, The MIT Press, Cambridge, Massachusetts, 1995.
BIBLIOGRAPHY
[19] P. O. Hoyer, “Non-negative matrix factorization with sparseness con-straints,” Journal of Machine Learning Research, vol. 5, pp. 1457–1469, November 2004.
[20] D. Guillamet and J. Vitri`a, “Non-negative matrix factorization for face recognition,” Escrig Monferrer, M. T., Toledo, F., Golobardes, E.
(Eds.), Topics in Artificial Intelligence. Springer-Verlag Series: Lecture Notes in Artificial Intelligence, vol. 2504, pp. 336–344, Castello de la Plana, 2002.
[21] D. Guillamet and J. Vitrigrave(a), “Classifying faces with non-negative matrix factorization,” Proceedings of the 5th Catalan Conference for Artificial Intelligence (CCIA 2002), pp. 24–31, Castello de la Plana, 2002.
[22] Xiaorong Pu, Zhang Yi, Ziming Zheng, Wei Zhou, and Mao Ye, “Face recognition using fisher non-negative matrix factorization with sparse-ness constraints,” Advances in Neural Networks - ISNN 2005: Second International Symposium on Neural Networks, Chongqing, China, May 30 - June 1, 2005, Proceedings, Part II Lecturer notes in computer sci-ence, vol. 3497, pp. 112–117, April 2005.
[23] Y. Wang, Y. Jia, C. Hu, and M. Turk, “Non-negative matrix factoriza-tion frame work for face recognifactoriza-tion,” Internafactoriza-tional Journal of Pattern Recognition and Artificial Intelligence, vol. 19, no. 4, pp. 1–17, 2005.
[24] I. Buciu and I. Pitas, “A new sparse image representation algorithm
BIBLIOGRAPHY
on Machine Learning for Signal Processing, Sao Luis, Brasil, pp. 539–
456, 2005.
[25] S. Zaferious, A. Tefas, I. Buciu, and I. Pitas, “Class-specific discriminant non-negative matrix factorization for frontal face verification,” Proceed-ings of 2005 International Conference on Advance in Pattern Recogni-tion (ICAPR 2005), Bath, United Kingdom, 2005.
[26] Menaka Rajapakse, J. Tan and Jagath C. Tajapakse, “Color channel encodign with NMF for face recognition,” Proceedings of the Interna-tional Conference Image Processing (Singapore Suntec City Convention Center, October 24–27, 2004.), pp. 2007–2010.
[27] Wei Xu, Win Liu, and Yihong Gong, “Document clustering based on non-negative matrix factorization,” Proceedings of the 26th annual in-ternational ACM SIGIR conference on Research and development in information retrieval, July 28–August 01, 2003, Toronto, Canada.
[28] Jeffrey Ho, Ming-Hsuan Yang, Jongwoo Lim, Kuang-Chih Lee, and David Kriegman, “Clustering Appearances of Objects Under Varying Il-lumination Conditions,” Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 11–18, 2003.
[29] D. Donono and V. Stodden. “When does non-negative matrix factor-ization give a correct decomposition into parts?” Proceedings of NIPS workshop on ICA, 2003.