Abstract：Traditionally, an (n1*n2) image is represented by a vector in the Euclidean space R(n1*n2), thus the spatial relationships between pixels in an image are ignored. In this paper, the images are presented as points in the tensor space Rn1Rn2. Then, a semi-supervised dimensionality reduction algorithm is put forward based on pairwise constraints (must-link and cannot-link)between the images. The data in the reduced space preserve the local structure of the data manifold well. Finally, experimental results on face datasets validate the effectiveness of the proposed algorithm.
[1] Duda R O, Hart P E, Stork D G. Pattern Classification. 2nd Edition. New York, USA: John Wiley & Sons, 2000 [2] He Xiaofei, Niyogi P. Locality Preserving Projections [EB/OL]. [2003-12-01]. http://books.nips.cc/papers/files/nips16/NIPS2002.AA20.pdf [3] Yang Jian, Zhang Daoqiang, Frangi A F, et al. Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition. IEEE Trans on Pattern Analysis and Machine Intelligence, 2004, 26(1): 131-137 [4] Zhang Daoqiang, Zhou Zhihua. (2D)2PCA: 2-Directional 2-Dimensional PCA for Efficient Face Representation and Recognition. Neurocomputing, 2005, 69(1/2/3): 224-231 [5] Zhang Daoqiang, Chen Songcan, Liu Jun. Representing Image Matrices: Eigenimages vs. Eigenvectors // Proc of the 2nd International Symposium on Neural Networks. Chongqing, China, 2005, Ⅱ: 659-664 [6] He Xiaofei, Cai Deng, Niyogi P. Tensor Subspace Analysis [EB/OL]. [2008-05-12].http://www.cs.uiuc.edu/homes/dengcai2/Data/data.html [7] He Xiaofei, Cai Deng, Liu Haifeng, et al. Image Clustering with Tensor Representation // Proc of the 13th Annual ACM International Conference on Multimedia. Hilton, Singapore, 2005: 132-140 [8] Cai Deng, He Xiaofai, Han Jiawei. Subspace Learning Based on Tensor Analysis. Technical Report, 2572, Urbana-Champaign, USA: University of Illinois. Department of Computer Science, 2005 [9] Ye Jieping, Janardan R, Li Qi. Two-Dimensional Linear Discriminant Analysis [EB/OL]. [2004-12-13]. http://books.nips.cc/papers/files/nips17/NIPS2004_0205.pdf [10] Zhu Xiaojin. Semi-Supervised Learning Literature Survey. Technical Report, 1530, Madison, USA: University of Wisconsin. Department of Computer Sciences, 2006 [11] Wagstaff K, Cardie C, Rogers S, et al. Constrained K-means Clustering with Background Knowledge // Proc of the 18th International Conference on Machine Learning. Williamstown, USA, 2001: 577-584 [12] Xing E P, Ng A Y, Jordan M I, et al. Distance Metric Learning, with Application to Clustering with Side-Information [EB/OL]. [2003-12-12]. http://ai.stanford.edu/~ang/papers/nips02-metric.pdf [13] Yu Shipeng, Yu Kai, Tresp V, et al. Supervised Probabilistic Principal Component Analysis // Proc of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Philadelphia, USA, 2006: 464-473 [14] Cai Deng, He Xiaofei, Han Jiawei. Semi-Supervised Discriminant Analysis [EB/OL]. [2007-10-14]. http://www.cs.uiuc.edu/homes/dengcai2/Publication/Conference/ICCV07_dengcai_SDA.pdf [15] Sugiyama M, Ide T, Nakajima S, et al. Semi-Supervised Local Fisher Discriminant Analysis for Dimensionality Reduction // Proc of the 12th Pacific-Asia Conference on Knowledge Discovery and Data Mining. Osaka, Japan, 2008: 333-344 [16] Zhang Daoqiang, Zhou Zhihua, Chen Songcan. Semi-Supervised Dimensionality Reduction [EB/OL]. [2007-07-31]. http://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/sdm07.pdf [17] Ham H J, Lee D D, Saul L K. Semi-Supervised Alignment of Manifolds [EB/OL]. [2005-01-06]. http://cs.used.edu/~saul/papers/semi_aistats05.pdf [18] Yang Xin, Fu Haoying, Zha Hongyuan, et al. Semi-Supervised Nonlinear Dimensionality Reduction // Proc of the 23rd International Conferences on Machine Learning. Pittsburgh, USA, 2006: 1065-1072 [19] Handl J, Knowles J. Semi-Supervised Feature Selection via Multiobjective Optimization // Proc of the International Joint Conferences on Neural Networks. Vancouver, Canada, 2006: 3319-3326 [20] Zhao Zheng, Liu Huan. Semi-Supervised Feature Selection via Spectral Analysis [EB/OL]. [2007-04-26]. http://www.slam.org/proceeding/datamining/2007/dm07-075ZHAOLIV.pdf [21] Tian Zongruo. Tensor Analysis. Xi'an, China: Northwestern Industry University Press, 2005 (in Chinese) (田宗若.张量分析.西安:西北工业大学出版社, 2005) [22] Georghiades A S, Belhumeur P N, Kriegman D J. From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose. IEEE Trans on Pattern Analysis and Machine Intelligence, 2001, 23(6): 643-660 [23] Georghiades A S, Belhumeur P N, Kriegman D J. From Few to Many: Generative Models for Recognition under Variable Pose and Illumination // Proc of the 4th IEEE International Conference on Automatic Face and Gesture Recognition. Grenoble, France, 2000: 277-284
2009, Vol. 22 
