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
Artificial Intelligence and Dimensionality Reduction: Tools for Approaching Future Communications
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Improvement of variables interpretability in kernel PCA
Marie-Agnès Dillies,S. Déjean +1 more
TL;DR: The proposed methodology, kernel PCA Interpretable Gradient (KPCA-IG), proved to be a valid alternative to select influential variables in high-dimensional high-throughput datasets, potentially unravelling new biological and medical biomarkers.
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Kernel multimodal discriminant analysis for speaker verification
Min-Seok Kim,IL-Ho Yang,Ha-Jin Yu +2 more
- 14 Mar 2010
TL;DR: This paper proposes a robust speaker feature extraction method using kernel multimodal Fisher discriminant analysis ( kernel MFDA), which has been designed to have the characteristics both of kernel principal component analysis (PCA) and kernel Fisher discriminating analysis (kernel FDA).
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Kernel Principal Components Analysis for Early Identification of Gear Tooth crack
He Qian,Yibing Liu,Peng Lv +2 more
- 23 Oct 2006
TL;DR: In this article, a case of gear fault diagnosis was studied by Kernel Principal Component Analysis (KPCA) and the feature value was firstly extracted from vibration signals of the gearbox under the condition of continue running, and then KPCA was used to extract the information of gear crack fault.
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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.
2.8K
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.
2.6K