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This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA.
LIII. on lines and planes of closest fit to systems of points in space
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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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The scree test for the number of factors
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Singular value decomposition and least squares solutions
Golub, Gene H and Reinsch, Christian · 1970
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Learning representations by back-propagating errors
Rumelhart, David E, Hinton, Geoffrey E, and Williams, Ronald J · 1986
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Face recognition using eigenfaces
Turk, Matthew A and Pentland, Alex P · 1991
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Local representation theory: Modular representations as an introduction to the local representation theory of finite groups , volume 11
Alperin, Jonathan L · 1993
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On the early history of the singular value decomposition
Stewart, Gilbert W · 1993
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Kernel principal component analysis
Schölkopf, Bernhard, Smola, Alexander, and Müller, Klaus-Robert · 1997
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Nonlinear component analysis as a kernel eigenvalue problem
Schölkopf, Bernhard, Smola, Alexander, and Müller, Klaus-Robert · 1998
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The role of Occam’s razor in knowledge discovery
Domingos, Pedro · 1999
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High-dimensional data analysis: The curses and blessings of dimensionality
Donoho, David L · 2000
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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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Face recognition using kernel eigenfaces
Yang, M-H, Ahuja, Narendra, and Kriegman, David · 2000
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Learning kernel classifiers: theory and algorithms
Herbrich, Ralf · 2001
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Automatic choice of dimensionality for pca
Minka, Thomas P · 2001
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Sparse kernel principal component analysis
Tipping, Michael E · 2001
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Laplacian eigenmaps for dimensionality reduction and data representation
Belkin, Mikhail and Niyogi, Partha · 2003
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The haar wavelet transform: its status and achievements
Stanković, Radomir S and Falkowski, Bogdan J · 2003
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Convex optimization
Boyd, Stephen and Vandenberghe, Lieven · 2004
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Latent semantic analysis
Dumais, Susan T · 2004
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A kernel view of the dimensionality reduction of manifolds
Ham, Ji Hun, Lee, Daniel D, Mika, Sebastian, and Schölkopf, Bernhard · 2004
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Principal component analysis
Abdi, Hervé and Williams, Lynne J · 2010
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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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Principal component analysis
Jolliffe, Ian · 2011
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Principal component analysis based methods in bioinformatics studies
Ma, Shuangge and Dai, Ying · 2011
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Open Problems in Spectral Dimensionality Reduction
Strange, Harry and Zwiggelaar, Reyer · 2014
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An analysis of the viola-jones face detection algorithm
Wang, Yi-Qing · 2014
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Hein, Matthias and Bousquet, Olivier · 2004
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Measuring statistical dependence with Hilbert-Schmidt norms
Gretton, Arthur, Bousquet, Olivier, Smola, Alex, and Schölkopf, Bernhard · 2005
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Prediction by supervised principal components
Bair, Eric, Hastie, Trevor, Paul, Debashis, and Tibshirani, Robert · 2006
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Dimensionality reduction: a short tutorial
Ghodsi, Ali · 2006
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Probability and random processes for electrical and computer engineers
Gubner, John A · 2006
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Sparse principal component analysis
Zou, Hui, Hastie, Trevor, and Tibshirani, Robert · 2006
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Statistical learning with sparsity: the lasso and generalizations
Tibshirani, Robert, Wainwright, Martin, and Hastie, Trevor · 2015
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Trace class operators and Hilbert-Schmidt operators
Bell, Jordan · 2016
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Deep learning
Goodfellow, Ian, Bengio, Yoshua, and Courville, Aaron · 2016
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Critical object recognition in millimeter-wave images with robustness to rotation and scale
Mohammadzade, Hoda, Ghojogh, Benyamin, Faezi, Sina, and Shabany, Mahdi · 2017
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Sparse supervised principal component analysis (sspca) for dimension reduction and variable selection
Sharifzadeh, Sara, Ghodsi, Ali, Clemmensen, Line H, and Ersbøll, Bjarne K · 2017
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Exploring new forms of random projections for prediction and dimensionality reduction in big-data regimes
Karimi, Amir-Hossein · 2018
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Srp: Efficient class-aware embedding learning for large-scale data via supervised random projections
Karimi, Amir-Hossein, Wong, Alexander, and Ghodsi, Ali · 2018
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Classification course, department of statistics and actuarial science, university of Waterloo
Ghodsi, Ali · 2019
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Data visualization course, department of statistics and actuarial science, university of Waterloo
Ghodsi, Ali · 2019
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Instance ranking and numerosity reduction using matrix decomposition and subspace learning
Ghojogh, Benyamin and Crowley, Mark · 2019
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Parametric PCA for unsupervised metric learning
Levada, Alexandre LM · 2020
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