Book Chapter10.1007/BFB0020217
Kernel Principal Component Analysis
Bernhard Schölkopf,Alexander J. Smola,Klaus-Robert Müller +2 more
- 08 Oct 1997
- pp 583-588
2.6K
TL;DR: A new method for performing a nonlinear form of Principal Component Analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
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Abstract: A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible d-pixel products in images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.
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Citations
Review of Dimension Reduction Methods
Salifu Nanga,Ahmed Tijani Bawah,Benjamin Ansah Acquaye,Mac-Issaka Billa,Francis Delali Baeta,Nii Afotey Odai,Samuel Kwaku Obeng,Ampem Darko Nsiah +7 more
- 08 Jul 2021
TL;DR: This study sought to review the characteristics, strengths, weaknesses, variants, applications areas and data types applied on the various Dimension Reduction techniques.
•Proceedings Article
Dimensionality Reduction for Spectral Clustering
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- 14 Jun 2011
TL;DR: This work introduces an augmented form of spectral clustering in which an explicit projection operator is incorporated in the relaxed optimization functional and optimize this functional over both the projection and the spectral embedding.
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning
Morgan A. Schmitz,Matthieu Heitz,Nicolas Bonneel,Fred Maurice Ngolè Mboula,David Coeurjolly,Marco Cuturi,Gabriel Peyré,Jean-Luc Starck +7 more
TL;DR: In this paper, a nonlinear dictionary learning method for histograms in the probability simplex is proposed, which uses displacement interpolations between dictionary atoms to reconstruct histograms using so-called Wasserstein barycenters.
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Network-based classification of ADHD patients using discriminative subnetwork selection and graph kernel PCA.
TL;DR: A discriminative subnetwork selection method is proposed to directly mine those frequent and discrim inative subnetworks from the whole brain networks of ADHD and normal control groups and can improve the performance significantly comparing to the state-of-the-art methods.
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Recognising trajectories of facial identities using kernel discriminant analysis
TL;DR: Kernel discriminant analysis, which employs the kernel technique to perform linear discriminantAnalysis in a high-dimensional feature space, is developed to extract the significant nonlinear features which maximise the between- class variance and minimise the within-class variance.
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References
Support-Vector Networks
Corinna Cortes,Vladimir Vapnik +1 more
TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
A training algorithm for optimal margin classifiers
Bernhard E. Boser,Isabelle Guyon,Vladimir Vapnik +2 more
- 01 Jul 1992
TL;DR: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented, applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions.
Nonlinear component analysis as a kernel eigenvalue problem
TL;DR: A new method for performing a nonlinear form of principal component analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
Application of the Karhunen-Loeve procedure for the characterization of human faces
Michael Kirby,Lawrence Sirovich +1 more
TL;DR: The use of natural symmetries (mirror images) in a well-defined family of patterns (human faces) is discussed within the framework of the Karhunen-Loeve expansion, which results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix.
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Simplified neuron model as a principal component analyzer
TL;DR: A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived.
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