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This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants.
Eigenvalue and generalized eigenvalue problems: Tutorial
Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark · 1903
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Feature selection and feature extraction in pattern analysis: A literature review
Ghojogh, Benyamin, Samad, Maria N, Mashhadi, Sayema Asif, Kapoor, Tania, Ali, Wahab, Karray, Fakhri, and Crowley, Mark · 1905
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Introduction to statistical pattern recognition
Fukunaga, Keinosuke · 1990
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On the early history of the singular value decomposition
Stewart, Gilbert W · 1993
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Interior-point polynomial algorithms in convex programming
Nesterov, Yurii and Nemirovskii, Arkadii · 1994
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The nature of statistical learning theory
Vapnik, Vladimir · 1995
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Semidefinite programming
Vandenberghe, Lieven and Boyd, Stephen · 1996
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Segmentation using eigenvectors: a unifying view
Weiss, Yair · 1999
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Nonlinear dimensionality reduction by locally linear embedding
Roweis, Sam T and Saul, Lawrence K · 2000
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A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, Joshua B, De Silva, Vin, and Langford, John C · 2000
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The effect of the input density distribution on kernel-based classifiers
Williams, Christopher and Seeger, Matthias · 2000
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Laplacian eigenmaps and spectral techniques for embedding and clustering
Belkin, Mikhail and Niyogi, Partha · 2001
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On spectral clustering: Analysis and an algorithm
Ng, Andrew, Jordan, Michael, and Weiss, Yair · 2001
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The kernel trick for distances
Schölkopf, Bernhard · 2001
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Kernel matrix completion by semidefinite programming
Graepel, Thore · 2002
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Learning with kernels: support vector machines, regularization, optimization, and beyond
Schölkopf, Bernhard, Smola, Alexander J, and Bach, Francis · 2002
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Global versus local methods in nonlinear dimensionality reduction
De Silva, Vin and Tenenbaum, Joshua B · 2003
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Think globally, fit locally: unsupervised learning of low dimensional manifolds
Saul, Lawrence K and Roweis, Sam T · 2003
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Learning eigenfunctions links spectral embedding and kernel PCA
Bengio, Yoshua, Delalleau, Olivier, Roux, Nicolas Le, Paiement, Jean-François, Vincent, Pascal, and Ouimet, Marie · 2004
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Convex optimization
Boyd, Stephen, Boyd, Stephen P, and Vandenberghe, Lieven · 2004
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A kernel view of the dimensionality reduction of manifolds
Ham, Jihun, Lee, Daniel D, Mika, Sebastian, and Schölkopf, Bernhard · 2004
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Learning the kernel matrix with semidefinite programming
Lanckriet, Gert RG, Cristianini, Nello, Bartlett, Peter, Ghaoui, Laurent El, and Jordan, Michael I · 2004
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Learning a kernel matrix for nonlinear dimensionality reduction
Weinberger, Kilian Q, Sha, Fei, and Saul, Lawrence K · 2004
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Unsupervised learning of image manifolds by semidefinite programming
Weinberger, KQ and Saul, LK · 2004
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Action respecting embedding
Bowling, Michael, Ghodsi, Ali, and Wilkinson, Dana · 2005
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Multidimensional scaling
Cox, Michael AA and Cox, Trevor F · 2008
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CVX: Matlab software for disciplined convex programming, 2008
Grant, Michael, Boyd, Stephen, and Ye, Yinyu · 2008
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Relaxed maximum-variance unfolding
Hou, Chenping, Jiao, Yuanyuan, Wu, Yi, and Yi, Dongyun · 2008
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Multidimensional scaling, Sammon mapping, and Isomap: Tutorial and survey
Ghojogh, Benyamin, Ghodsi, Ali, Karray, Fakhri, and Crowley, Mark · 2009
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Guided locally linear embedding
Alipanahi, Babak and Ghodsi, Ali · 2011
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Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds
Barshan, Elnaz, Ghodsi, Ali, Azimifar, Zohreh, and Jahromi, Mansoor Zolghadri · 2011
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Measuring statistical dependence with Hilbert-Schmidt norms
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Locally linear embedding and its variants: Tutorial and survey
Ghojogh, Benyamin, Ghodsi, Ali, Karray, Fakhri, and Crowley, Mark · 2011
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Maximum covariance unfolding: Manifold learning for bimodal data
Mahadevan, Vijay, Wong, Chi, Pereira, Jose, Liu, Tom, Vasconcelos, Nuno, and Saul, Lawrence · 2011
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A general framework for dimensionality-reducing data visualization mapping
Bunte, Kerstin, Biehl, Michael, and Hammer, Barbara · 2012
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On a connection between maximum variance unfolding, shortest path problems and Isomap
Paprotny, Alexander and Garcke, Jochen · 2012
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Geometric structure of high-dimensional data and dimensionality reduction , volume 5
Wang, Jianzhong · 2012
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Nonlinear process monitoring and fault isolation using extended maximum variance unfolding
Liu, Yuan-Jui, Chen, Tao, and Yao, Yuan · 2014
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Open Problems in Spectral Dimensionality Reduction
Strange, Harry and Zwiggelaar, Reyer · 2014
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Parametric nonlinear dimensionality reduction using kernel t-sne
Gisbrecht, Andrej, Schulz, Alexander, and Hammer, Barbara · 2015
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Developments of two supervised maximum variance unfolding algorithms for process classification
Wei, Chihang, Chen, Junghui, and Song, Zhihuan · 2016
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A summary of the kernel matrix, and how to learn it effectively using semidefinite programming
Karimi, Amir-Hossein · 2017
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Unsupervised and supervised principal component analysis: Tutorial
Ghojogh, Benyamin and Crowley, Mark · 2019
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Data Reduction Algorithms in Machine Learning and Data Science
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