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This is a tutorial and survey paper on kernels, kernel methods, and related fields.
Eigenvalue and generalized eigenvalue problems: Tutorial
Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark · 1903
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Grundzüge einer allgemeinen theorie der linearen integralrechnungen I
Hilbert, David · 1904
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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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Fisher and kernel Fisher discriminant analysis: Tutorial
Ghojogh, Benyamin, Karray, Fakhri, and Crowley, Mark · 1906
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Über die auflösung linearer gleichungen mit unendlich vielen unbekannten
Schmidt, Erhard · 1908
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Functions of positive and negative type and their connection with the theory of integral equations
Mercer, J · 1909
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Über die praktische auflösung von integralgleichungen mit anwendungen auf randwertaufgaben
Nyström, Evert J · 1930
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Theory of reproducing kernels
Aronszajn, Nachman · 1950
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Sur certains espaces vectoriels topologiques
Bourbaki, Nicolas · 1950
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On information and sufficiency
Kullback, Solomon and Leibler, Richard A · 1951
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The Stone-Weierstrass theorem
De Branges, Louis · 1959
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Theoretical foundations of the potential function method in pattern recognition learning
Aizerman, Mark A, Braverman, E. M., and Rozonoer, L. I · 1964
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Some results on Tchebycheffian spline functions
Kimeldorf, George and Wahba, Grace · 1971
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Methods of modern mathematical physics: Functional analysis
Reed, Michael and Simon, Barry · 1972
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A ‘short’ proof of the Riesz representation theorem
Garling, DJH · 1973
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Theory of pattern recognition
Vapnik, Vladimir and Chervonenkis, Alexey · 1974
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Cauchy and the spectral theory of matrices
Hawkins, Thomas · 1975
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The numerical treatment of integral equations
Baker, Christopher TH · 1978
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Etude des produits scalaires sur l’espace des mesures: estimation par projections
Guilbart, Christian · 1978
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Introduction to Banach spaces and their geometry
Beauzamy, Bernard · 1982
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Quantum mechanics in Hilbert space
Prugovecki, Eduard · 1982
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Harmonic analysis on semigroups: theory of positive definite and related functions , volume 100
Berg, Christian, Christensen, Jens Peter Reus, and Ressel, Paul · 1984
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Spline models for observational data
Wahba, Grace · 1990
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A training algorithm for optimal margin classifiers
Boser, Bernhard E, Guyon, Isabelle M, and Vapnik, Vladimir N · 1992
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Multivariate density estimation: theory, practice, and visualization
Scott, David W · 1992
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Local representation theory: Modular representations as an introduction to the local representation theory of finite groups
Alperin, Jonathan L · 1993
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The fundamental theorem of linear algebra
Strang, Gilbert · 1993
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Fundamentals of neural networks: architectures, algorithms and applications
Fausett, Laurene V · 1994
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Kernel smoothing
Wand, Matt P and Jones, M Chris · 1994
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Searching for the kernel of a polygon—a competitive strategy
Icking, Christian and Klein, Rolf · 1995
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The nature of statistical learning theory
Vapnik, Vladimir · 1995
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Introduction to radial basis function networks
Orr, Mark J. L · 1996
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Semidefinite programming
Vandenberghe, Lieven and Boyd, Stephen · 1996
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Integral probability metrics and their generating classes of functions
Müller, Alfred · 1997
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A tutorial on support vector machines for pattern recognition
Burges, Christopher JC · 1998
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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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Learning with kernels , volume 4
Smola, Alex J and Schölkopf, Bernhard · 1998
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Bayesian classification with Gaussian processes
Williams, Christopher KI and Barber, David · 1998
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Fisher discriminant analysis with kernels
Mika, Sebastian, Ratsch, Gunnar, Weston, Jason, Scholkopf, Bernhard, and Mullers, Klaus-Robert · 1999
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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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Classes of kernels for machine learning: a statistics perspective
Genton, Marc G · 2001
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The kernel trick for distances
Schölkopf, Bernhard · 2001
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On the influence of the kernel on the consistency of support vector machines
Steinwart, Ingo · 2001
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Using the Nyström method to speed up kernel machines
Williams, Christopher and Seeger, Matthias · 2001
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Digital image processing
Gonzalez, Rafael C and Woods, Richard E · 2002
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Kernel-based reinforcement learning
Ormoneit, Dirk and Sen, Śaunak · 2002
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Beginning functional analysis
Saxe, Karen · 2002
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Learning with kernels: support vector machines, regularization, optimization, and beyond
Schölkopf, Bernhard and Smola, Alexander J · 2002
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Support vector machines are universally consistent
Steinwart, Ingo · 2002
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Function replacement vs. kernel trick
Ma, Junshui · 2003
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Kernelization algorithms for the vertex cover problem: Theory and experiments
Abu-Khzam, Faisal N, Collins, Rebecca L, Fellows, Micheal R, Langston, Micheal A, Suters, W Henry, and Symons, Christopher T · 2004
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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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Multidimensional scaling, Sammon mapping, and Isomap: Tutorial and survey
Ghojogh, Benyamin, Ghodsi, Ali, Karray, Fakhri, and Crowley, Mark · 2009
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The elements of statistical learning: data mining, inference, and prediction
Hastie, Trevor, Tibshirani, Robert, and Friedman, Jerome · 2009
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Low-rank kernel learning with Bregman matrix divergences
Kulis, Brian, Sustik, Mátyás A, and Dhillon, Inderjit S · 2009
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Sampling techniques for the Nyström method
Kumar, Sanjiv, Mohri, Mehryar, and Talwalkar, Ameet · 2009
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Normalized kernels as similarity indices
Ah-Pine, Julien · 2010
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Consistent nonparametric tests of independence
Gretton, Arthur and Györfi, László · 2010
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Spectral grouping using the Nyström method
Fowlkes, Charless, Belongie, Serge, Chung, Fan, and Malik, Jitendra · 2004
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Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces
Fukumizu, Kenji, Bach, Francis R, and Jordan, Michael I · 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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Kernels, associated structures and generalizations
Hein, Matthias and Bousquet, Olivier · 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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Distance measures for PCA-based face recognition
Perlibakas, Vytautas · 2004
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Making large-scale Nyström approximation possible
Li, Mu, Kwok, James Tin-Yau, and Lü, Baoliang · 2010
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Topological vector spaces
Narici, Lawrence and Beckenstein, Edward · 2010
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Hilbert space embeddings and metrics on probability measures
Sriperumbudur, Bharath K, Gretton, Arthur, Fukumizu, Kenji, Schölkopf, Bernhard, and Lanckriet, Gert RG · 2010
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Clustered Nyström method for large scale manifold learning and dimension reduction
Zhang, Kai and Kwok, James T · 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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Universal algebra: Fundamentals and selected topics
Bergman, Clifford · 2011
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Reproducing kernel Hilbert spaces in probability and statistics
Berlinet, Alain and Thomas-Agnan, Christine · 2011
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On the mathematical properties of the structural similarity index
Brunet, Dominique, Vrscay, Edward R, and Wang, Zhou · 2011
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A novel greedy algorithm for Nyström approximation
Farahat, Ahmed, Ghodsi, Ali, and Kamel, Mohamed · 2011
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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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Digital Filters: Basics and Design
Schlichtharle, Dietrich · 2011
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Universality, characteristic kernels and RKHS embedding of measures
Sriperumbudur, Bharath K, Fukumizu, Kenji, and Lanckriet, Gert RG · 2011
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A kernel two-sample test
Gretton, Arthur, Borgwardt, Karsten M, Rasch, Malte J, Schölkopf, Bernhard, and Smola, Alexander · 2012
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Sampling methods for the Nyström method
Kumar, Sanjiv, Mohri, Mehryar, and Talwalkar, Ameet · 2012
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Prediction: Machine learning and statistics (MIT 15.097), lecture on kernels
Rudin, Cynthia · 2012
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Equivalence of distance-based and RKHS-based statistics in hypothesis testing
Sejdinovic, Dino, Sriperumbudur, Bharath, Gretton, Arthur, and Fukumizu, Kenji · 2013
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Operating Systems: Principles and Practice
Anderson, Thomas and Dahlin, Michael · 2014
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Kernel methods and machine learning
Kung, Sun Yuan · 2014
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Open Problems in Spectral Dimensionality Reduction
Strange, Harry and Zwiggelaar, Reyer · 2014
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Greedy column subset selection for large-scale data sets
Farahat, Ahmed K, Elgohary, Ahmed, Ghodsi, Ali, and Kamel, Mohamed S · 2015
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Generative moment matching networks
Li, Yujia, Swersky, Kevin, and Zemel, Rich · 2015
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Double Nyström method: An efficient and accurate Nyström scheme for large-scale data sets
Lim, Woosang, Kim, Minhwan, Park, Haesun, and Jung, Kyomin · 2015
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Less is more: Nyström computational regularization
Rudi, Alessandro, Camoriano, Raffaello, and Rosasco, Lorenzo · 2015
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Machine learning for quantum mechanics in a nutshell
Rupp, Matthias · 2015
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Trace class operators and Hilbert-Schmidt operators
Bell, Jordan · 2016
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Deep learning , volume 1
Goodfellow, Ian, Bengio, Yoshua, Courville, Aaron, and Bengio, Yoshua · 2016
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Kernel mean embedding of distributions: A review and beyond
Muandet, Krikamol, Fukumizu, Kenji, Sriperumbudur, Bharath, and Schölkopf, Bernhard · 2016
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Wasserstein generative adversarial networks
Arjovsky, Martin, Chintala, Soumith, and Bottou, Léon · 2017
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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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Literature survey on low rank approximation of matrices
Kishore Kumar, N and Schneider, Jan · 2017
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Multi-scale Nyström method
Lim, Woosang, Du, Rundong, Dai, Bo, Jung, Kyomin, Song, Le, and Park, Haesun · 2018
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An introduction to kernel-based learning algorithms
Müller, Klaus-Robert, Mika, Sebastian, Tsuda, Koji, and Schölkopf, Bernhard · 2018
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Reproducing kernels of Sobolev spaces on ℝ d \mathbb{R}^{d} and applications to embedding constants and tractability
Novak, Erich, Ullrich, Mario, Woźniakowski, Henryk, and Zhang, Shun · 2018
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Lecture: Recasting principal components
Oldford, Wayne · 2018
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Digital signal processing with Kernel methods
Rojo-Álvarez, José Luis, Martínez-Ramón, Manel, Marí, Jordi Muñoz, and Camps-Valls, Gustavo · 2018
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Kernel distribution embeddings: Universal kernels, characteristic kernels and kernel metrics on distributions
Simon-Gabriel, Carl-Johann and Schölkopf, Bernhard · 2018
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Kernelization: theory of parameterized preprocessing
Fomin, Fedor V, Lokshtanov, Daniel, Saurabh, Saket, and Zehavi, Meirav · 2019
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Unsupervised and supervised principal component analysis: Tutorial
Ghojogh, Benyamin and Crowley, Mark · 2019
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Metrizing weak convergence with maximum mean discrepancies
Simon-Gabriel, Carl-Johann, Barp, Alessandro, and Mackey, Lester · 2020
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Advanced stationary and non-stationary kernel designs for domain-aware Gaussian processes
Noack, Marcus M and Sethian, James A · 2021
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