南京大学学报(自然科学版) ›› 2017, Vol. 53 ›› Issue (6): 1091.
郑 玮1,2,杨万扣3,邵 斐1*,赵 炜1
Zheng Wei1,2,Yang Wankou3,Shao Fei1*,Zhao Wei1
摘要: 以稀疏表示为代表的回归分类方法对于高斯噪声具有较好的鲁棒性,但容易受到训练样本中离群点数据的影响导致欠拟合或过拟合.通过探索余弦函数对离群数据呈现的周期不敏感特性,使用余弦函数来刻画回归残差,并在复数域空间进行稀疏回归,提出了三角稀疏回归分类器(TSRC)模型.考虑到模型的非凸特性,普通的迭代算法难以获得全局最优解.因此,通过三角函数演算与核函数技巧将TSRC转化为一个凸优化问题,使用交替方向乘子法(ADMM)对模型进行求解,核函数的计算过程从核空间角度解释了模型对离群点鲁棒的本质原因,通过欧拉公式能够完全避开复数域的计算过程,从而起到加速的作用.在AR,Extend-YaleB及NUST-RF带有遮挡和光照变化的人脸识别数据集上进行了识别率与速度的实验,验证了所提出模型的有效性,在Extend-YaleB数据集上测试了所提出方法在不同尺度的训练样本下的运行效率,并与现阶段先进方法进行了对比.
[1] 周志华.机器学习.北京:清华大学出版社,2016,60-63.(Zhou Z H.Machine learning.Beijing:Tsinghua University Press,2016,60-63.) [2] Naseem I,Togneri R,Bennamoun M.Linear regression for face recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence,2010,32(11):2106-2112. [3] Wright J,Yang A Y,Ganesh A,et al.Robust face recognition via sparse representation.IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(2):210-227. [4] Yang J,Luo L,Qian J J,et al.Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes.IEEE Transactions on Pattern Analysis and Machine Intelligence,2017,39(1):156-171. [5] Mairal J,Bach F,Ponce J,et al.Supervised dictionary learning.arXiv:0809.3083,2009. [6] Zhang Q,Li B X.Discriminative K-SVD for dictionary learning in face recognition.In:Proceedings of 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.San Francisco,CA,USA:IEEE,2010:2691-2698. [7] Yang J C,Yu K,Gong Y H,et al.Linear spatial pyramid matching using sparse coding for image classification.In:Proceedings of 2009 IEEE Conference on Computer Vision and Pattern Recognition.Miami,FL,USA:IEEE,2009:1794-1801. [8] Elad M,Aharon M.Image denoising via sparse and redundant representations over learned dictionaries.IEEE Transactions on Image Processing,2006,15(12):3736-3745. [9] Guyon I,Elisseeff A.An introduction to variable and feature selection.Journal of Machine Learning Research,2003,3:1157-1182. [10] Donoho D L.De-noising by soft-thresholding.IEEE Transactions on Information Theory,1995,41(3):613-627. [11] 陈宝林.最优化理论与算法.第2版.北京:清华大学出版社,2005,232-238.(Chen B L.Optimization theory and algorithm.The 2nd Editon.Beijing:Tsinghua University Press,2005,232-238.) [12] Eckstein J.Augmented Lagrangian and alternating direction methods for convex optimization:A tutorial and some illustrative computational results.Rutgers University:RUTCOR Research Reports,2012,32. [13] Lee H,Battle A,Raina R,et al.Efficient sparse coding algorithms.In:Advances in Neural Information Processing Systems 19,Proceedings of the 20th Annual Conference on Neural Information Processing Systems.Vancouver,Canada:NIPS,2006,801-808. [14] Naseem I,Togneri R,Bennamoun M.Robust regression for face recognition.Pattern Recognition,2012,45(1):104-118. [15] Li X X,Dai D Q,Zhang X F,et al.Structured sparse error coding for face recognition with occlusion.IEEE Transactions on Image Processing,2013,22(5):1889-1900. [16] He R,Zheng W S,Hu B G,et al.A regularized correntropy framework for robust pattern recognition.Neural Computation,2011,23(8):2074-2100. [17] He R,Zheng W S,Hu B G.Maximum correntropy criterion for robust face recognition.IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(8):1561-1576. [18] Liwicki S,Tzimiropoulos G,Zafeiriou S,et al.Euler principal component analysis.International Journal of Computer Vision,2013,101(3):498-518. [19] Gao S,Tsang I,Chia L T.Kernal sparse representation for image classification and face recognition.In:The 11th European Conference on Computer Version(ECCV 2010).Crete,Greece:Springer,2010:1-14. [20] Boyd S,Parikh N,Chu E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers.Foundations and Trends? in Machine Learning,2011,3(1):1-122. [21] Lin T Y,Ma S Q,Zhang S Z.On the global linear convergence of the admm with multiblock variables.SIAM Journal on Optimization,2015,25(3):1478-1497. [22] Jia K,Chan T H,Ma Y.Robust and practical face recognition via structured sparsity.In:Fitzgibbon A,Lazebnik S,Perona P,et al.12th European Conference on Computer Version.Springer Berlin Heidelberg,2012:331-344. [23] Martinez A M,Benavente R.The AR face database.CVC Technical Report #24,1998. [24] Lee K C,Ho J,Kriegman D J.Acquiring linear subspaces for face recognition under variable lighting.IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(5):684-698. |
No related articles found! |
|