Book Chapter10.1007/BFB0020217
Kernel Principal Component Analysis
Bernhard Schölkopf,Alexander J. Smola,Klaus-Robert Müller +2 more
- 08 Oct 1997
- pp 583-588
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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
An efficient P300 detection algorithm based on Kernel Principal Component Analysis-Support Vector Machine
TL;DR: In this article , features were obtained from wavelet coefficients and feature dimensions were reduced, thereby enhancing the speed of classification along with a manifold improvement in the accuracy of P300 signal classification.
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A method for regularization of evolutionary polynomial regression
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TL;DR: Experiments show that evolutionary polynomial regression with regularization is able to achieve better fitting and needs less computation time than plain EPR, and a set of experiences to compare both flavors of EPR against other methods including linear regression, regression trees and support vector regression.
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A new algorithm for redundancy minimisation in geo-environmental data
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TL;DR: A new unsupervised learning algorithm to reduce the redundancy in the input space is proposed, based on the adaptation of a space filling criterion called the coverage measure, to select the most useful subset of the independent variables in a dataset by reducing the existing redundancy.
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•Proceedings Article
Generative Kernel PCA.
Joachim Schreurs,Johan A. K. Suykens +1 more
- 01 Jan 2018
TL;DR: A generative kernel PCA which can be used to generate new data, as well as denoise a given training dataset, in a non-probabilistic setting is introduced.
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Robust decision making and its applications in machine learning
Huan Xu
- 01 Jan 2009
TL;DR: The theoretical front, it is proved that both SVM and Lasso are special cases of robust optimization, and such robustness interpretation implies consistency and sparsity naturally.
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.
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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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