完备的双子空间边界近邻鉴别分析

J4 ›› 2014, Vol. 36 ›› Issue (07): 1357-1362.

完备的双子空间边界近邻鉴别分析

林玉娥1，李敬兆1，梁兴柱1，林玉荣2

(1.安徽理工大学计算机科学与工程学院，安徽淮南 232001;2.哈尔滨工业大学航天学院，黑龙江哈尔滨 150001)

收稿日期:2013-01-17 修回日期:2013-04-07 出版日期:2014-07-25 发布日期:2014-07-25
基金资助:
国家自然科学基金资助项目(61170060)；安徽省自然科学基金资助项目(1208085QF123，11040606M135)；安徽省高等学校自然科学基金资助项目(KJ2012Z084，KJ2011A083)；安徽理工大学中青年学术骨干资助项目

A complete dual subspace marginal
neighborhood discriminant analysis algorithm

LIN Yue1，LI Jingzhao1，LIANG Xingzhu1，LIN Yurong2

(1.School of Computer Science & Engineering,Anhui University of Science and Technology,Huainan 232001;2.School of Astronautics,Harbin Institute of Technology,Harbin 150001,China)

Received:2013-01-17 Revised:2013-04-07 Online:2014-07-25 Published:2014-07-25

摘要/Abstract

摘要：

针对边界Fisher鉴别分析算法不能够有效解决小样本问题,提出了一种完备的双子空间边界近邻鉴别分析算法。该算法通过理论分析将MFA的目标函数分解成两部分，对此目标函数的求解，首先要对高维样本进行PCA降维至一个低维子空间, 而这一过程并不损失任何有效的鉴别信息，对此通过定理1和定理2进行了证明；然后再分别求出类内边界近邻互补子空间的两投影矩阵。最后人脸库上的实验结果表明了所提方法的有效性。

关键词: 边界Fisher鉴别分析, 小样本问题, 双子空间, 目标函数

Abstract:

Aiming at the shortcomings that the marginal Fisher discriminant analysis algorithm can not effectively solve the small sample size problem, a complete dual subspace marginal neighborhood discriminant analysis algorithm is proposed. According to the theoretical analysis, the proposed algorithm breaks down the criterion function of the Fisher discriminant analysis into two parts. To solve the criterion function, the algorithm firstly uses PCA to project highdimensional samples into a lowdimensional subspace. In the lowdimensional subspace, the objective function does not lose any effective discriminant information, which is proved by theorem 1 and theorem 2. Secondly, projection matrix from the complementary subspace of withinclass marginal neighborhood is calculated. Finally, the experimental results on face database demonstrate the effectiveness of the proposed algorithm.

Key words: marginal Fisher discriminant analysis;the small sample size problem;dual subspace;the criterion function

林玉娥1，李敬兆1，梁兴柱1，林玉荣2. 完备的双子空间边界近邻鉴别分析[J]. J4, 2014, 36(07): 1357-1362.

LIN Yue1，LI Jingzhao1，LIANG Xingzhu1，LIN Yurong2. A complete dual subspace marginal
neighborhood discriminant analysis algorithm [J]. J4, 2014, 36(07): 1357-1362.

参考文献

［1］He X F, Yan S C,Hu Y.Face recognition using Laplacianfaces ［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(3):328340.
［2］Zhang H, Sun S, Jing Z, et al. Local structure based supervised feature extraction［J］. Pattern Recognition, 2006,39(8):15461550.
［3］Zhu L,Zhu S N. Face recognition based on orthogonal discriminant locality preserving projections［J］.Neurocomputing, 2007,70(9):15431546.
［4］Yan S, Xu D, Zhang B, et al. Graph embedding:A general framework for dimensionality reduction ［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1):4051.
［5］Xu D,Yan S, Tao D. Marginal fisher analysis and its variants for human gait recognition and contentbased image retrieval［J］.IEEE Transactions on Image Processing, 2007,16(11):28112821.
［6］Belhumeur P N, Hespanha J P, Kriegam D J. Eigenfaces vs. Fisherfaces:Recognition using class specific linear projection ［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence,1997,19(7):711720.
［7］Xie Jun, Liu Jian. A new local discriminant projection method［J］. Chinese Journal of Computers,2011,31(11):22432250.(in Chinese)
［8］Fang B, Cheng M, Tang Y Y. Improving the discriminant ability of local margin based learning method by incorporating the global betweenclass separability criterion［J］. Neurocomputing,2009,73(1):536541.
［9］Yu Yaoliang, Zhang Liming. Orthogonal MFA and uncorrelated MFA［J］.Pattern Recognition and Artificial Intelligence,2008,21(5):604608.(in Chinese)
［10］Lin Kezheng,Wang Huixin,Bu Xuena.Discriminant maximum margin criterion based on locality preserving projections［J］. Pattern Recognition and Artificial Intelligence, 2010,23(2):178185.(in Chinese)
［11］Lu Guifu,Lin Zhong, Jin Zhong. Face recognition based on twodimensional maximum difference marginal fisher analysis［J］. Computer Science, 2010,35(7):251253.(in Chinese)
［12］Lu G F, Lin Z, Jin Z. Face recognition using discriminant locality preserving projections based on maximum margin criterion ［J］. Pattern Recognition, 2010,43 (3):35723579.
［13］Tao Y T, Yang J. Quotient vs. difference:Comparison between the two discriminant criteria ［J］. Neurocomputing, 2010, 73(1012):18081817.
［14］Lu Guifu, Lin Zhong, Jin Zhong. Optimal discriminant analysis based on kernel extension of graph embedding and face recognition［J］. Journal of Software,2011,22(7):15611570. (in Chinese)
［15］http://www.nist.gov/humanid/feret/feret_master.html.
［16］http://cobweb.ecn.purdue.edu/~aleix/aleix_face_DB.html.
［17］Yan Deqin, Liu Shenglan, Li Yanyan. An embedding dimension reduction algorithm based on sparse analysis［J］. Acta Automatica Sinica, 2011, 37(11):13061312.(in Chinese)
附中文参考文献：
［7］谢钧,刘剑.一种新的局部判别投影方法［J］.计算机学报,2011,31(11):22432250.
［9］于耀亮,张立明.正交MFA和不相关MFA［J］.模式识别与人工智能,2008,21(5):604608.
［10］林克正,王慧鑫,卜雪娜.基于局部保持投影的鉴别最大间距目标［J］.模式识别与人工智能,2010,23(2):178185.
［11］卢桂馥,林忠,金忠.基于最大差值的二维边界Fisher的人脸识别［J］.计算机科学，2010,35(7):251253.
［14］卢桂馥,林忠,金忠.基于核化图嵌入的最佳鉴别分析与人脸识别［J］.软件学报,2011,22(7):15611570.
［17］闫德勤, 刘胜蓝, 李燕燕. 一种基于稀疏嵌入分析的降维方法［J］. 自动化学报, 2011, 37(11):13061312.

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