|
|
|
| Compressive Sensing Based Neighborhood Embedding |
| JIA Jiong1, ZHENG Zhong-Long1, YANG Jie2 |
1.Department of Computer Science and Technology,Zhejiang Normal University,Jinhua 321004
2.Institute of Image Processing and Pattern Recognition,Shanghai Jiaotong University,Shanghai 200240 |
|
|
|
|
Abstract How to construct local neighborhoods is one of the key points of spectral-manifold based algorithms. For example, locally linear embedding (LLE), one of the traditional manifold learning algorithms, constructs the local relationships through KNN or ε criterion. Motivated by compressive sensing theory, the strategy of neighborhood construction is proposed based on the linear combination of l2 and l1, which is called compressive sensing based neighborhood embedding (CSNE). The proposed strategy can not only be applied to LLE, but also to other spectral learning methods while neighborhoods need to be constructed. In addition, the semi-supervised CSNE algorithm is presented while the un-labeled data are taken into account. The results of visualization and classification experiments on several datasets demonstrates the competitive results of the proposed algorithm compared with PCA、LDA、LPP and S-Isomap.
|
|
Received: 11 May 2011
|
|
|
|
|
|
[1] Wright J,Ganesh A,Yang A,et al.Robust Face Recognition via Sparse Representation.IEEE Trans on Pattern Analysis and Machine Intelligence,2009,31(2): 1-21
[2] TurkM,Pentland A.Eigenfaces for Recognition.Journal of Cognitive Neuroscience,1991,3(1): 71-86
[3] 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
[4] 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
[5] Roweis S T,Saul L K.Nonlinear Dimensionality Reduction by Locally Linear Embedding.Science,2000,290(5500): 2323-2326
[6] Tenenbaum J B,Silva V D,Langford J C.A Global Geometric Framework for Nonlinear Dimensionality Reduction.Science,2000,290(5500): 2319-2323
[7] Zhang Xhenyue,Zha Hongyuan.Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment.SIAM Journal of Scientific Computing,2005,26(1): 313-338
[8] Belkin M,Niyogi P.Laplacian Eigenmaps for Dimensionality Reduction and Data Representation.Neural Computation,2003,15(6): 1373-1396
[9] Yan Shuicheng,Xu Dong,Zhang Benyu,et al.Graph Embedding and Extension: A General Framework for Dimensionality Reduction.IEEE Trans on Pattern Analysis and Machine Intelligence,2007,29(1): 40-51
[10] Cheng Bin,Yang Jianchao,Yan Shuicheng,et al.Learning with l1-Graph for Image Analysis.IEEE Trans on Image Processing,2010,19(4): 858-866
[11] Smith K.Mind-Reading with a Brain Scan [EB/OL].[2008-3-5].http://www.nature.com/news/2008/080305/full/news.2008.650.html
[12] Candes E,Rudelson M,Tao T,et al.Error Correction via Linear Programming // Proc of the 46th Annual IEEE Symposium on Foundations of Computer Science.Pittsburgh,USA,2005: 295-308
[13] Donoho D.For Most Large Underdetermined Systems of Linear Equations,the Minimal l1-Norm Solution is also the Sparsest Solution.Communications on Pure and Applied Mathematics,2006,59(6): 797-829
[14] Sanja F,Leonardis A.Combining Reconstructive and Discriminative Subspace Methods for Robust Classification and Regression by Subsampling.IEEE Trans on Pattern Analysis and Machine Intelligence,2006,28(3): 337-350
[15] Jiao Licheng,Bo Liefeng,Wang Ling.Fast Sparse Approximation for Least Square Support Vector Machine.IEEE Trans on Neural Networks,2007,18(3): 685-697
[16] Abdallah S,Plumbley M.Unsupervised Analysis of Polyphonic Music by Sparse Coding.IEEE Trans on Neural Networks,2006,17(1): 179-196
[17] Li Y,Cichocki A,Amari S.Lind Estimation of Channel Parameters and Source Components for Egg Signals: A Sparse Factorization Approach.IEEE Trans on Neural Networks,2006,17(1): 419-431
[18] Zou H,Hastie T,Tibshirani R.Sparse Principal Component Analysis.Journal of Computational and Graphical Statistics,2006,15(2): 265-286
[19] Moghaddam B,Weiss Y,Avidan S.Generalized Spectral Bounds for Sparse LDA // Proc of the International Conference on Machine Learning.Pittsburgh,USA,2006: 641-648
[20] Tibshirani R.Regression Shrinkage and Selection via the Lasso.Journal of Royal Statistics Society,1996,58(1): 267-288
[21] Zhou Zhihua,Xu Junming.On the Relation between Multi-Instance Learning and Semi-Supervised Learning // Proc of the International Conference on Machine Learning.Corvallis,USA,2007: 211-218
[22] Zhang Dan,Wang Jingdang,Wang Fei,et al.Semi-Supervised Classification with Universum // Proc of the SIAM International Conference on Data Mining.Auckland,New Zealand,2008: 323-333
[23] Belkin M,Matveeva I,Niyogi P.Regularization and Semi-Supervised Learning on Large Graphs // Proc of the Conference on Learning Theory.Banff,Canada,2004: 624-638
[24] Zhu X,Ghahramani Z,Lafferty J.Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions // Proc of the International Conference on Machine Learning.Washington,USA,2003: 912-919
[25] Guo Zhen,Zhang Zhongfei,Xing E.Semi-Supervised Learning Based on Semi-Parametric Regularization // Proc of the SIAM International Conference on Data Mining.Auckland,New Zealand,2008: 132-142
[26] Yan Shuicheng,Wang Huan.Semi-Supervised Learning by Sparse Representation // Proc of the SIAM International Conference on Data Mining.Sparks,USA,2009: 792-801
[27] Cai Deng,He Xiaofei,Han Jiawei.Semi-Supervised Discriminant Analysis // Proc of the International Conference on Computer Vision.Rio de Janeiro,Brazil,2007: 1-7
[28] Geng Xin,Zhan Dechuan,Zhou Zhihua.Supervised Nonlinear Dimensionality Reduction for Visualization and Classification.IEEE Trans on Systems,Man and Cybernetics,2005,35(6): 1098-1107 |
|
|
|
2012, Vol. 25 
