A Flexible and Effective Linearization Method for Subspace Learning

In the past decades, a large number of subspace learning or dimension reduction methods [2, 16, 20, 32, 34, 37, 44] have been proposed. Principal component analysis (PCA) [32] pursues the directions of maximum variance for optimal reconstruction. Linear discriminant analysis (LDA) [2], as a supervised algorithm, aims to maximize the inter-class scatter and at the same time minimize the intra-class scatter. Due to utilization of label information, LDA is experimentally reported to outperform PCA for face recognition, when sufficient labeled face images are provided [2].

[1]  Dacheng Tao,et al.  Discriminative Locality Alignment , 2008, ECCV.

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

[3]  Harry Shum,et al.  Face Hallucination: Theory and Practice , 2007, International Journal of Computer Vision.

[4]  Dong Xu,et al.  Semi-Supervised Dimension Reduction Using Trace Ratio Criterion , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

[6]  Jiawei Han,et al.  Spectral Regression: A Regression Framework for Efficient Regularized Subspace Learning , 2009 .

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

[8]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[9]  Feiping Nie,et al.  Semi-supervised orthogonal discriminant analysis via label propagation , 2009, Pattern Recognit..

[10]  Christos Faloutsos,et al.  Semi-Supervised Learning Based on Semiparametric Regularization , 2008, SDM.

[11]  Feiping Nie,et al.  Learning a Mahalanobis distance metric for data clustering and classification , 2008, Pattern Recognit..

[12]  Hongyuan Zha,et al.  Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment , 2002, ArXiv.

[13]  Bernhard Schölkopf,et al.  Local learning projections , 2007, ICML '07.

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

[15]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Feiping Nie,et al.  Efficient and Robust Feature Selection via Joint ℓ2, 1-Norms Minimization , 2010, NIPS.

[17]  D. B. Graham,et al.  Characterising Virtual Eigensignatures for General Purpose Face Recognition , 1998 .

[18]  Feiping Nie,et al.  Nonlinear Dimensionality Reduction with Local Spline Embedding , 2009, IEEE Transactions on Knowledge and Data Engineering.

[19]  Xin Yang,et al.  Semi-supervised nonlinear dimensionality reduction , 2006, ICML.

[20]  Feiping Nie,et al.  A general kernelization framework for learning algorithms based on kernel PCA , 2010, Neurocomputing.

[21]  Mikhail Belkin,et al.  Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering , 2001, NIPS.

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

[23]  H. Zha,et al.  Principal manifolds and nonlinear dimensionality reduction via tangent space alignment , 2004, SIAM J. Sci. Comput..

[24]  Tzuu-Hseng S. Li,et al.  Robust $H_{\infty}$ Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Xuelong Li,et al.  Patch Alignment for Dimensionality Reduction , 2009, IEEE Transactions on Knowledge and Data Engineering.

[26]  Feiping Nie,et al.  Trace Ratio Problem Revisited , 2009, IEEE Transactions on Neural Networks.

[27]  Jiawei Han,et al.  Spectral Regression for Efficient Regularized Subspace Learning , 2007, 2007 IEEE 11th International Conference on Computer Vision.

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

[29]  Mikhail Belkin,et al.  Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples , 2006, J. Mach. Learn. Res..

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

[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]  Yi Yang,et al.  A Multimedia Retrieval Framework Based on Semi-Supervised Ranking and Relevance Feedback , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[33]  Mikhail Belkin,et al.  Linear Manifold Regularization for Large Scale Semi-supervised Learning , 2005 .

[34]  Tong Zhang,et al.  Linear prediction models with graph regularization for web-page categorization , 2006, KDD '06.

[35]  Wei Liu,et al.  Transductive Component Analysis , 2008, 2008 Eighth IEEE International Conference on Data Mining.

[36]  Alex Pentland,et al.  Face recognition using eigenfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[37]  Ivor W. Tsang,et al.  Flexible Manifold Embedding: A Framework for Semi-Supervised and Unsupervised Dimension Reduction , 2010, IEEE Transactions on Image Processing.

[38]  Avrim Blum,et al.  The Bottleneck , 2021, Monopsony Capitalism.

[39]  W. Marsden I and J , 2012 .

[40]  Feiping Nie,et al.  Semi-Supervised Classification via Local Spline Regression , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[41]  Wei Chu,et al.  Relational Learning with Gaussian Processes , 2006, NIPS.

[42]  Xuelong Li,et al.  A unifying framework for spectral analysis based dimensionality reduction , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[43]  Mikhail Belkin,et al.  Beyond the point cloud: from transductive to semi-supervised learning , 2005, ICML.

[44]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[45]  Bernhard Schölkopf,et al.  Learning with Local and Global Consistency , 2003, NIPS.

[46]  Jiawei Han,et al.  Semi-supervised Discriminant Analysis , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[47]  Carlos Castillo,et al.  Web spam identification through content and hyperlinks , 2008, AIRWeb '08.

[48]  Feiping Nie,et al.  Orthogonal locality minimizing globality maximizing projections for feature extraction , 2009 .

[49]  Vikas Sindhwani,et al.  Document-Word Co-regularization for Semi-supervised Sentiment Analysis , 2008, 2008 Eighth IEEE International Conference on Data Mining.

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

[51]  Xuelong Li,et al.  Semisupervised Dimensionality Reduction and Classification Through Virtual Label Regression , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[52]  Xuelong Li,et al.  Discriminant Locally Linear Embedding With High-Order Tensor Data , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[53]  Xiaojin Zhu,et al.  --1 CONTENTS , 2006 .

[54]  Deli Zhao,et al.  Formulating LLE using alignment technique , 2006, Pattern Recognit..