A Novel Dimensionality Reduction Method Based on Tensor and Lorentzian Geometry
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摘要: 统的基于向量的降维算法,将大小为m×n的灰度图像,作为Rm×n中的向量进行处理.但这种表示方法往往造成图像像素空间局部信息的丢失,因此不能很好地描述图像的结构信息.本质上,灰度图像可以看成是一个二阶张量,而图像的各种特征(如Gabor和LBP特征等)往往需要用更高阶的张量来描述.本文从图像特征的张量表示出发,将新近提出的洛仑兹投影判别法(Lorentziandiscriminant projection, LDP)推广到张量空间中,提出张量LDP.对于灰度图像,该方法直接利用图像的灰度矩阵(二阶张量)进行运算,从而很好地保持了图像像素的局部结构信息.另外,该方法还可以自然地推广到高维张量空间来处理更复杂的图像特征,如Gabor和LBP特征等.经人脸和纹理识别实验的验证,该算法效率高且能达到较高的识别率.Abstract: Traditional vector-based dimensionality reduction algorithms consider an m×n image as a high dimensional vector in Rm×n. However, because this representation usually causes the lost of the local spatial information, it can not describe the image well. Intrinsically, an image is a 2D tensor and some feature extracted from the image (e.g. Gabor feature, LBP feature) may be a higher tensor. In this paper, we consider the nature of the image feature and propose the tensor Lorentzian discriminant projection algorithm, which can be considered as the tensor generation of the newly proposed Lorentzian discriminant projection (LDP). With regard to an image, this algorithm directly uses the hue matrix to compute, so it keeps the local spatial information well. In addition, this method can be naturally extended to the higher tensor space to deal with more complicated image features, such as Gabor feature and LBP feature. The experimental results on face and texture recognition show that our algorithm achieves better recognition accuracy while being much more efficient.
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Key words:
- Tensor /
- dimensionality reduction /
- Lorentzian ge-ometry /
- face recognition /
- texture recognition
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[1] Yang Jian, Yang Jing-Yu, Ye Hui. Theory of Fisher linear discriminant analysis and its application. Acta Automatica Sinica, 2003, 29(4): 481-493(杨健, 杨静宇, 叶晖. Fisher线性鉴别分析的理论研究及其应用. 自动化学报, 2003, 29(4): 481-493)[2] Su Zhi-Xun, Liu Yan-Yan, Liu Xiu-Ping, Zhou Xiao-Jie. Image feature extraction and recognition based on fuzzy CCA. Computer Engineering, 2007, 33(16): 144-146(苏志勋, 刘艳艳, 刘秀平, 周晓杰. 基于模糊CCA的图像特征提取和识别. 计算机工程, 2007, 33(16): 144-146)[3] Turk M A, Pentland A P. Face recognition using eigenfaces. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Maui, USA: IEEE, 1991. 586-591[4] Belhumeur P N, Hespanha J P, Kriegman D J. Eigenface vs. Fisher-faces: recognition using class specific linear projection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(7): 711-720[5] He X, Yan S, Hu Y, Niyogi P, Zhang H. Face recognition using Laplacianfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(3): 328-340[6] Li H, Jiang T, Zhang K. Efficient and robust feature extraction by maximum margin criterion. IEEE Transactions on Neural Networks, 2003, 17(1): 157-165[7] Wu Xiu-Yong, Xu Ke, Xu Jin-Wu. Automatic recognition method of surface defects based on Gabor wavelet and kernel locality preserving projections. Acta Automatica Sinica, 2010, 36(3): 438-441(吴秀永, 徐科, 徐金梧. 基于Gabor小波和核保局投影算法的表面缺陷自动识别方法. 自动化学报, 2010, 36(3): 438-441)[8] Li Le, Zhang Yu-Jin. Linear projection-based non-negative matrix factorization. Acta Automatica Sinica, 2010, 36(1): 23-39(李乐, 章毓晋. 基于线性投影结构的非负矩阵分解. 自动化学报, 2010, 36(1): 23-39)[9] Wu Feng, Zhong Yan, Wu Quan-Yuan. Online classification framework for data stream based on incremental kernel principal component analysis. Acta Automatica Sinica, 2010, 36(4): 534-542(吴枫, 仲妍, 吴泉源. 基于增量核主成分分析的数据流在线分类框架. 自动化学报, 2010, 36(4): 534-542)[10] Liu Bo, Zhang Hong-Bin. A manifold unfolding method based on boundary constraints. Acta Automatica Sinica, 2010, 36(4): 488-498(刘波, 张鸿宾. 一种基于边界约束的流形展开方法. 自动化学报, 2010, 36(4): 488-498)[11] Wang Lei, Zou Bei-Ji, Peng Xiao-Ning. Tunneled latent variables method for facial action unit tracking. Acta Automatica Sinica, 2009, 35(2): 198-201(王磊, 邹北骥, 彭小宁. 针对表情动作单元跟踪的隧道隐变量法. 自动化学报, 2009, 35(2): 198-201)[12] Zhang W, Lin Z, Tang X. Learning semi-riemannian metrics for semisupervised feature extraction. IEEE Transactions on Knowledge Discovery and Engineering, 2011, 23(4): 600-611[13] Cai D, He X, Han J. Subspace Learning Based on Tensor Analysis, Technical Report No. UIUCDCS-R-2005-2572, Department of Computer Science, University of Illinois at Urbana-Champaign, USA, 2005[14] He X, Cai D, Niyogi P. Tensor subspace analysis. Advances in Neural Information Processing Systems. Massachusetts: The MIT Press, 2005[15] Yan S, Xu D, Yang Q, Zhang L, Tang X, Zhang H. Discriminant analysis with tensor representation. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington D.C., USA: IEEE, 2005. 526-532[16] Yan S, Xu D, Zhang B, Zhang H, 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[17] Liu R, Su Z, Lin Z, Hou X. Lorentzian discriminant projection and its applications. In: Proceedings of the 9th Asian Conference on Computer Vision. Xi'an, China: Springer, 2009. 311-320[18] O'Neill B. Semi-riemannian Geometry with Applications to Relativity. New York: Academic Press, 1983[19] Lathauwer L, Moor B, Vandewalle J. A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications, 2000, 21(4): 1253-1278[20] Ojala T, Pietikainen M, Maenpaa T. Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(7): 971-987
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