A New Supervised Manifold Learning Algorithm Based on MMC and LSE
-
摘要: 针对局部样条嵌入算法 (Local spline embedding,LSE) 存在样本外点学习和无监督模式学习问题,本文提出了一种新颖的正交局部样条判别投影算法 (O-LSDP).该算法通过引入明确的线性映射关系,构建平移缩放模型,以及正交化特征子空间,从而使该算法能够应用于模式分类问题并显著改善了算法的分类识别能力.在标准人 脸数据库和植物叶片数据库上的实验结果验证了该算法的有效性与可行性.Abstract: In order to circumvent the two major shortcomings of the original local spline embedding (LSE) algorithm, i.e., out-of-sample and unsupervised learning, we proposed a novel feature extraction algorithm called orthogonal local spline discriminant projection (O-LSDP). By introducing an explicit linear mapping, constructing different translation and resealing models for different classes as well as orthogonality feature subspace, the O-LSDP not only inherits the advantages of LSE which uses local tangent space as a representation of the local geometry so as to preserve the local structure, but also makes full use of class information and orthogonal subspace to significantly improve the discriminant power. Experimental results on standard face databases and plant leaf data set demonstrate the feasibility and effectiveness of the proposed algorithm.
-
[1] Tenenbaum J B, de Silva V, Langford J C. A global geometric framework for nonlinear dimensionality reduction. Science, 2000, 290(5500): 2319-2323 [2] Roweis S T, Saul L K. Nonlinear dimensionality reduction by locally linear embedding. Science, 2000, 290(5500): 2323-2326 [3] Donoho D L, Grimes C. Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(10): 5591-5596 [4] Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 2003, 15(6): 1373-1396 [5] Weinberger K Q, Saul L K. Unsupervised learning of image manifolds by semidefinite programming. In: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR-04). Washington D. C., USA: IEEE, 2004. 988-995 [6] Zhang Z Y, Zha H Y. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM Journal of Scientific Computing, 2005, 26(1): 313-338 [7] Lin T, Zha H B. Riemannian manifold learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008, 30(5): 796-809 [8] Xiang S M, Nie F P, Zhang C S, Zhang C X. Nonlinear dimensionality reduction with local spline embedding. IEEE Transactions on Knowledge and Data Engineering, 2009, 21(9): 1285-1298 [9] Carreira-Perpiñán M A. The elastic embedding algorithm for dimensionality reduction. In: Proceedings of the 27th International Conference on Machine Learning. Haifa, Israel: IMLS, 2010. 167-174. [10] Luo D J, Ding C, Nie F P, Huang H. Cauchy graph embedding. In: Proceedings of the 28th International Conference on Machine Learning. Haifa, Israel: IMLS, 2011. 553-560 [11] Zhang S W, Lei Y K, Wu Y H. Semi-supervised locally discriminant projection for classification and recognition. Knowledge-Based Systems, 2011, 24(2): 341-346 [12] Zhang S W, Lei Y K, Wu Y H, Yang J A. Modified orthogonal discriminant projection for classification. Neurocomputing, 2011, 74(17): 3690-3694 [13] Zhan P, Qiao H, Zhang B. An improved local tangent space alignment method for manifold learning. Pattern Recognition Letters, 2011, 32(2): 181-189 [14] Lei Y K, You Z H, Dong T B, Jiang Y X, Yang J A. Increasing reliability of protein interactome by fast manifold embedding. Pattern Recognition Letters, 2013, 34(4): 372-379 [15] Yan S C, Xu D, Zhang B Y, Zhang H J, Yang Q, Lin S. Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1): 40-51 [16] He X F, Yan S C, Hu Y X, Niyogi P, Zhang H J. Face recognition using laplacianfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(3): 328-340 [17] Kokiopoulou E, Saad Y. Orthogonal neighborhood preserving projections: a projection-based dimensionality reduction technique. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(12): 2143-2156 [18] Choi H, Choi S. Robust kernel Isomap. Pattern Recognition, 2007, 40(3): 853-8620 [19] Meng De-Yu, Xu Chen, Xu Zong-Ben. A new manifold reconstruction method based on Isomap. Chinese Journal of Computers, 2010, 33(3): 545-555 (孟德宇, 徐晨, 徐宗本. 基于Isomap的流形结构重建方法. 计算机学报, 2010, 33(3): 545-555) [20] Pan Y Z, Ge S S, Al Mamun A. Weighted locally linear embedding for dimension reduction. Pattern Recognition, 2009, 42(5): 798-811 [21] De Ridder D, Kouropteva O, Okun O, Pietikäinen M, Duin R P W. Supervised locally linear embedding. In: Proceedings of the 2003 Joint International Conference on Artificial Neural Networks and Neural Information Processing. Istanbul, Turkey: Springer-Verlag, 2003. 333-341 [22] Geng X, Zhan D C, Zhou Z H. Supervised nonlinear dimensionality reduction for visualization and classification. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2005, 35(6): 1098-1107 [23] Li X R, Jiang T, Zhang K S. Efficient and robust feature extraction by maximum margin criterion. IEEE Transactions on Neural Networks, 2006, 17(1): 157-165 [24] Duchon J. Constructive Theory of Functions of Several Variables. Berlin, Heidelberg: Springer, 1977. 85-100 [25] Söderkvist O. Computer Vision Classification of Leaves from Swedish Trees[Master dissertation], Linköping University, Linköping, 2001 [26] Ye J P. Characterization of a family of algorithms for generalized discriminant analysis on undersampled problems. Journal of Machine Learning Research, 2006, 6: 483-502 [27] Duchene J, Leclercq S. An optimal transformation for discriminant and principal component analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988, 10(6): 978-983 [28] Belhumeur P N, Hespanha J P, Kriegman D J. Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 711-720 [29] Cai D, He X, Han J. Using Graph Model for Face Analysis. University of Illinois Urbana-Champaign, Urbana, IL, Department of Computer Science, Technical Report, 2005 [30] Zhang T H, Yang J, Zhao D L, Ge X L. Linear local tangent space alignment and application to face recognition. Neurocomputing, 2007, 70(7-9): 1547-1553
点击查看大图
计量
- 文章访问数: 2400
- HTML全文浏览量: 76
- PDF下载量: 1735
- 被引次数: 0