Abstract Locality Preserving Projections (LPP) aims to preserve local structure of the data by constructing a nearest-neighbor graph. However,it is confronted with the difficulty of parameter selection in the process of graph construction. To solve this problem,an algorithm called parameter-free locality preserving projections (PLPP) is proposed. Firstly,a parameter-free graph construction strategy is designed,which can actively determine neighbors of each data point and assign corresponding edge weights. Then,with the proposed graph construction strategy,PLPP seeks an optimal transformation matrix to preserve local structure of the data in the low dimensional space. Since PLPP needs no parameters in graph construction and takes cosine distance as the similarity weight,it is more efficient and robust to outliers than LPP. Moreover,supervised PLPP (SPLPP) is proposed to improve the discriminant ability of PLPP by considering class information of samples. The experimental results on the ORL,FERET and AR face databases validate the effectiveness of PLPP and SPLPP.
[1] Turk M,Pentland A. Eigenfaces for Recognition. Journal of Cognitive Neuroscience,1991,3(1): 71-86 [2] Belhumeur P N,Hespanha J P,Kriegman D J. Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. IEEE Trans on Pattern Analysis and Machine Intelligence,1997,19(7): 711-720 [3] Roweis S T,Saul L K. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science,2000,290(5500): 2323-2326 [4] Cui Peng,Zhang Rubo. A Semi-Supervised Coefficient Selection Method for Face Recognition. Journal of Harbin Engineering University,2012,33(7): 855-861 (in Chinese) (崔 鹏,张汝波.半监督系数选择法的人脸识别.哈尔滨工程大学学报,2012,33(7): 855-861) [5] Belkin M,Niyogi P. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation,2003,15(6): 1373-1396 [6] Tenenbaum J B,de Silva V,Langford J C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science,2000,290(5500): 2319-2323 [7] He Xiaofei,Yan Shuicheng,Hu Yuxiao,et al. Face Recognition Using Laplacianfaces. IEEE Trans on Pattern Analysis and Machine Intelligence,2005,27(3): 328-340 [8] Yang Jian,Zhang D,Yang Jingyu,et al. Globally Maximizing,Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and Palm Biometrics. IEEE Trans on Pattern Analysis and Machine Intelligence,2007,29(4): 650-664 [9] Yu Weiwei,Teng Xiaolong,Liu Chongqing. Face Recognition Using Discriminant Locality Preserving Projections. Image and Vision Computing,2006,24(3): 239-248 [10］Li J B,Pan J S,Chu S C. Kernel Class-Wise Locality Preserving Projection. Information Science,2008,178(7): 1825-1835 [11] Yan Shuicheng,Xu Dong,Zhang Benyu,et al. Graph Embedding: A General Framework for Dimensionality Reduction. IEEE Trans on Pattern Analysis and Machine Intelligence,2007,29(1): 40-51 [12] Xu Yong,Zhong Aini,Yang Jian,et al. LPP Solution Schemes for Use with Face Recognition. Pattern Recognition,2010,43(12): 4165-4176 [13] Wang Sujing,Chen Huiling,Peng Xujun,et al. Exponential Locality Preserving Projections for Small Sample Size Problem. Neurocomputing,2011,74(17): 3654-3662 [14] Yu Guoxian,Peng Hong,Wei Jia,et al. Enhanced Locality Preserving Projections Using Robust Path Based Similarity. Neurocomputing,2011,74(4): 598-605 [15] Yang Bo,Chen Songcan. Sample-Dependent Graph Construction with Application to Dimensionality Reduction. Neurocomputing,2010,74(1/2/3): 301-314 [16] Dornaika F,Assoum A. Enhanced and Parameterless Locality Preserving Projections for Face Recognition. Neurocomputing,2013,99(1): 448-457 [17] Yin Jun,Zhou Jingbo,Jin Zhong. Principal Component Analysis and Kernel Principal Component Analysis Based on Cosine Angle Distance. Computer Engineering and Applications,2011,47(3): 9-12 (in Chinese) (殷 俊,周静波,金 忠.基于余弦角距离的主成分分析与核主成分分析.计算机工程与应用,2011,47(3): 9-12)
2013, Vol. 26 
