非負矩陣分解已被證明有益於描述人臉局部特徵的變化。在本篇論文中，我們的目標是要從人臉照片來做年齡估測。希望使用具有標籤資訊的非負矩陣分解來擷取人臉上與年齡相關的特徵。由於每個人的老化過程都不盡相同，要取出適合所有人年齡變化的特徵，不是一件容易的事情。為了克服這個困難，我們提出了新的方法，將我們所設計的限制條件與非負矩陣分解結合，來處理不同人擁有不同老化過程的問題。此外，我們還把此方法延伸至，當訓練樣本與測試樣本有年齡差距之人臉辨識問題上。藉由提出的方法，我們成功地擷取出在人臉上局部區域與年齡相關的特徵。並且從實驗結果看來，不論是在年齡估測或是有年齡差距之人臉辨識問題上，我們的方法皆優於大多數現有的方法

Nonnegative matrix factorization (NMF) tends to characterize local feature variation and has been shown to be better interpretable on facial images. In this thesis, to solve the facial age estimation problem, we propose to extract age-related features by using a supervised NMF. In addition, since different people usually have very different aging tendency, it is by no means an easy task to find a set of good age-related features feasible for all individuals. To overcome this difficulty, we further include a person-independent constraint and propose a new approach called person-independent supervised NMF (PISNMF) to characterize the aging properties. In addition, we also extend our proposed PISNMF to handle the age-invariant face recognition problem. We conduct PISNMF on FG-NET database and successfully extract the aging-related features. Our experiments show that the derived facial bases indeed characterize age-related local variations and the results of both age estimation and age-invariant face recognition outperform most existing methods.

[1] T. F. Cootes, G. J. Edwards, and C. J. Taylor, “Active Appearance Models,” in Proc. ECCV, vol. 2, pp. 484-498, 1998.
[2] D. Lee and H. Seung, “Algorithms for non-negative matrix factorization,” Advances in neural information processing systems, pp. 556–562, 2000.
[3] S. Joshi, S. Karthikeyan, B.S. Manjunath, S. Grafton and K.A. Kiehl, “Anatomical Parts-Based Regression Using Non-Negative Matrix Factorization,” IEEE International Conf. on CVPR, 2010.
[4] X. Geng, Z.H. Zhou, Y. Zhang, G. Li, and H. Dai, “Learning from Facial Aging Patterns for Automatic Age Estimation,” Proc.ACM Conf. on Multimedi , 2006.
[5] S. Yan, H. Wang, Y. Fu, J. Yan, X. Tang, and T.S. Huang, “Synchronized submanifold embedding for person-independent pose estimation and beyond,” IEEE Trans. on Image Processing., vol. 18, no. 1, pp. 202–210, Jan. 2009.
[6] Y. Zhang and D. Y. Yeung, “Multi-task warped Gaussian process for personalized age estimation,” IEEE Conference on CVPR, 2010.
[7] S. Yan, D. Xu, B. Zhang, Q. Yang, H. Zhang, and S. Lin, “Graph embedding and extensions: A general framework for dimensionality reduction,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, pp. 40–51, 2007.
[8] M. Belkin and P. Niyogi, “Laplacian eigenmaps and spectral techniques for embedding and clustering,” Advances in neural information processing systems, pp. 585–591, 2001.
[9] X. He and P. Niyogi, “Locality Preserving Projections,” Proc. Conf. Advances in Neural Information Processing Systems, 2003.
[10] S. Yan, H. Wang, X. Tang and T.S. Huang, “Learning Auto-Structured Regressor from Uncertain Nonnegative Labels,” IEEE International Conf. on Computer Vision, 2007.
[11] G. Guo, Y. Fu, T.S. Huang and C. Dyer. “Locally adjusted robust regression for human age estimation,” IEEE Workshop on WACV, 2008.
[12] A. Gunay and V. V. Nabiyev, “Automatic Age Classification with LBP,” Computer and Information Sciences, 2008.
[13] G. Guo, G. Mu, Y. Fu and T.S. Huang, “Human age estimation using bio-inspired features,” IEEE International Conf. on CVPR, 2009.
[14] C.-J. Lin, “Projected gradient methods for non-negative matrix factorization, ” Neural Computation, 19(2007), pp. 2756-2779.
[15] A. Lanitis and C.J. Taylor, “Towards Automatic Face Recognition, Robust to Aging Variation,” Proc. Fourth Int’l Conf. Automatic Face and Gesture Recognition, pp. 391-396, 2000.
[16] The FG-NET Aging database, http://www.fgnet.rsunit.com/
[17] C.-C. Chang and C.-J. Lin, “LIBSVM : a library for support vector machines,” ACM Transactions on Intelligent Systems and Technology, Vol. 2 Issue 3, April 2011. http://www.csie.ntu.edu.tw/~cjlin/libsvm
[18] J. Wright, A. Ganesh, A. Yang, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 31, no. 2, pp. 210–227, Feb. 2009.