All Title Author
Keywords Abstract

-  2016 

A Projection Algorithm with Local Preservation Based on L2 Norm

DOI: 10.7652/xjtuxb201602006

Keywords: 降维,局部保持投影,L2范数
dimensionality reduction
,locality preserving projections,L2 norm

Full-Text   Cite this paper   Add to My Lib


A projection algorithm with locality preserving projections based on the L2 norm (LPP??L2) is proposed to solve the problem that objective functions of traditional projection algorithms with local preservation (LPP) are based on the squared L2 norm and very sensitive to outliers. The weight matrix of the algorithm is recalculated using an iterative method and the objective function is also simplified, as a result, the optimized projection matrix is obtained. The algorithm converges to a local optimum in each iteration. The optimized projection matrix is used to project the original data into an optimal projection subspace with reduced dimension, while the characters of original data are preserved. Experimental results on synthesized data and a comparison with the LPP algorithm show that the LPP??L2 algorithm effectively reduces the data dimension and makes the algorithm more robust to outliers, it gains higher accurate and steady classification rate in face recognition, and a recognition rate of 80% is obtained


[1]  [1]张丽梅. 面向降维的图学习研究及应用 [D]. 南京: 南京航空航天大学, 2012.
[2]  [2]YAN Shuicheng, XU Dong, ZHANG Benyu, et al. Graph embedding and extensions: a general framework for dimensionality reduction [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1): 40??51.
[3]  [3]JOLLIFFE I T. Principal component analysis [M]. Berlin, Germany: Springer, 2002: 2??5.
[4]  [4]MARTINEZ A M, KAK A C. PCA versus LDA [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(2): 228??233.
[5]  [5]NIYOGI P, HE Xiaofei. Locality preserving projections [J]. Advances in Neural Information Processing Systems, 2003: 153??162.
[6]  [6]HE Xiaofei, YAN Shuicheng, HU Yuxiao, et al. Face recognition using Laplacian faces [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(3): 328??340.
[7]  [7]何晓飞. 人脸识别的几何观点: 拉普拉斯脸 [J]. 科学观察, 2010, 5(6): 67??68.
[8]  HE Xiaofei. Face recognition: Laplasse’s face [J]. Science Focus, 2010, 5(6): 67??68.
[9]  [8]PTUCHA R, TSAGKATAKIS G, SAVAKIS A. Manifold learning for simultaneous pose and facial expression recognition [C]∥Proceedings of the IEEE International Conference on Computer Vision. Piscataway, NJ, USA: IEEE, 2011: 3021??3024.
[10]  [9]TURK M, PENTLAND A. Eigenfaces for recognition [J]. Journal of Cognitive Neuroscience, 1991, 3(1): 71??86.
[11]  [10]RAO A, NOUSHATH S. Subspace methods for face recognition [J]. Computer Science Review, 2010, 4(1): 1??17. 
[12]  [11]NIE Feiping, WANG Hua, HUANG Heng, et al. Unsupervised and semi??supervised learning via L1??norm graph [C]∥Proceedings of the 2011 IEEE International Conference on Computer Vision. Piscataway, NJ, USA: IEEE, 2011: 2268??2273,
[13]  [12]HUANG Heng, XU Dong, NIE Feiping. Semi??supervised dimension reduction using trace ratio criterion [J]. IEEE Transactions on Neural Network Learning System, 2012, 23(3): 519??526.
[14]  [13]SYMEON N, ANASTASIOS T, LOANNIS P. Maximum margin projection subspace learning for visual data analysis [J]. IEEE Transactions on Image Processing, 2014, 23(10): 4413??4425.


comments powered by Disqus