Low-Rank Preserving Projections

As one of the most popular dimensionality reduction techniques, locality preserving projections (LPP) has been widely used in computer vision and pattern recognition. However, in practical applications, data is always corrupted by noises. For the corrupted data, samples from the same class may not be distributed in the nearest area, thus LPP may lose its effectiveness. In this paper, it is assumed that data is grossly corrupted and the noise matrix is sparse. Based on these assumptions, we propose a novel dimensionality reduction method, named low-rank preserving projections (LRPP) for image classification. LRPP learns a low-rank weight matrix by projecting the data on a low-dimensional subspace. We use the L21 norm as a sparse constraint on the noise matrix and the nuclear norm as a low-rank constraint on the weight matrix. LRPP keeps the global structure of the data during the dimensionality reduction procedure and the learned low rank weight matrix can reduce the disturbance of noises in the data. LRPP can learn a robust subspace from the corrupted data. To verify the performance of LRPP in image dimensionality reduction and classification, we compare LRPP with the state-of-the-art dimensionality reduction methods. The experimental results show the effectiveness and the feasibility of the proposed method with encouraging results.

[1]  Jiwen Lu,et al.  Regularized Locality Preserving Projections and Its Extensions for Face Recognition , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Nenghai Yu,et al.  Non-negative low rank and sparse graph for semi-supervised learning , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[3]  Anil K. Jain,et al.  Statistical Pattern Recognition: A Review , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[5]  Dacheng Tao,et al.  Large-Margin Multi-ViewInformation Bottleneck , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[7]  Kongqiao Wang,et al.  Distributed Object Detection With Linear SVMs , 2014, IEEE Transactions on Cybernetics.

[8]  Andy Harter,et al.  Parameterisation of a stochastic model for human face identification , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.

[9]  Zuowei Shen,et al.  Robust video denoising using low rank matrix completion , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[10]  Jiawei Han,et al.  Orthogonal Laplacianfaces for Face Recognition , 2006, IEEE Transactions on Image Processing.

[11]  Yuxiao Hu,et al.  Face recognition using Laplacianfaces , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Bo Geng,et al.  DAML: Domain Adaptation Metric Learning , 2011, IEEE Transactions on Image Processing.

[13]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[14]  Jian Yang,et al.  Constructing PCA Baseline Algorithms to Reevaluate ICA-Based Face-Recognition Performance , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Avinash C. Kak,et al.  PCA versus LDA , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[17]  Xuelong Li,et al.  General Tensor Discriminant Analysis and Gabor Features for Gait Recognition , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Zhixun Su,et al.  Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation , 2011, NIPS.

[19]  A. Martínez,et al.  The AR face databasae , 1998 .

[20]  Dacheng Tao,et al.  Multi-View Intact Space Learning , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Wai Keung Wong,et al.  Sparse Alignment for Robust Tensor Learning , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Xuelong Li,et al.  Geometric Mean for Subspace Selection , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Yousef Saad,et al.  Orthogonal Neighborhood Preserving Projections: A Projection-Based Dimensionality Reduction Technique , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Yanwei Pang,et al.  Learning Regularized LDA by Clustering , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Nenghai Yu,et al.  Face Recognition Using Neighborhood Preserving Projections , 2005, PCM.

[26]  Nenghai Yu,et al.  Neighborhood Preserving Projections (NPP): A Novel Linear Dimension Reduction Method , 2005, ICIC.

[27]  Changsheng Xu,et al.  Inductive Robust Principal Component Analysis , 2012, IEEE Transactions on Image Processing.

[28]  John Wright,et al.  Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization , 2009, NIPS.

[29]  Jian Yang,et al.  BDPCA plus LDA: a novel fast feature extraction technique for face recognition , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  Aleix M. Martinez,et al.  The AR face database , 1998 .

[31]  Stephen Lin,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Terence Sim,et al.  The CMU Pose, Illumination, and Expression Database , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Junfeng Yang,et al.  A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration , 2009, SIAM J. Imaging Sci..

[34]  Yuqing He,et al.  Semi-supervised LPP algorithms for learning-to-rank-based visual search reranking , 2015, Inf. Sci..

[35]  Feiping Nie,et al.  A unified framework for semi-supervised dimensionality reduction , 2008, Pattern Recognit..

[36]  Yong Yu,et al.  Robust Subspace Segmentation by Low-Rank Representation , 2010, ICML.

[37]  Lu Wang,et al.  Orthogonal Neighborhood Preserving Embedding for Face Recognition , 2007, 2007 IEEE International Conference on Image Processing.

[38]  Nicolas Le Roux,et al.  Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering , 2003, NIPS.

[39]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[40]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[41]  Xuelong Li,et al.  Ranking Graph Embedding for Learning to Rerank , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[42]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[43]  Kaizhu Huang,et al.  m-SNE: Multiview Stochastic Neighbor Embedding , 2011, IEEE Trans. Syst. Man Cybern. Part B.

[44]  WenAn Tan,et al.  Gabor feature-based face recognition using supervised locality preserving projection , 2007, Signal Process..

[45]  Daoqiang Zhang,et al.  Semi-Supervised Dimensionality Reduction ∗ , 2007 .

[46]  Shuicheng Yan,et al.  Neighborhood preserving embedding , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[47]  Xiaoyang Tan,et al.  Pattern Recognition , 2016, Communications in Computer and Information Science.

[48]  David J. Kriegman,et al.  Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection , 1996, ECCV.

[49]  Xuelong Li,et al.  Discriminative Orthogonal Neighborhood-Preserving Projections for Classification , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[50]  Kongqiao Wang,et al.  Robust CoHOG Feature Extraction in Human-Centered Image/Video Management System , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).