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
Tutorial on PCA and approximate PCA and approximate kernel PCA
TL;DR: In this paper , the mathematical foundation of classical PCA and its application to a small-sample-size scenario and a large dataset in a high-dimensional space scenario are discussed.
Feature Selection and Extraction for Malware Classification
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Training Quantum Embedding Kernels on Near-Term Quantum Computers.
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•Book
An introduction to kernel methods
Colin Campbell
- 01 Mar 2001
TL;DR: This Chapter describes how to use kernel methods for classification, regression and novelty detection and in each case it is found that training can be reduced to optimization of a convex cost function.
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•Journal Article
On the Use of Kernel PCA for Feature Extraction in Speech Recognition
Amaro A. de Lima,Heiga Zen,Yoshihiko Nankaku,Chiyomi Miyajima,Keiichi Tokuda,Tadashi Kitamura +5 more
TL;DR: This paper describes an approach in representing speech features as the projection of the extracted speech features mapped into a feature space via a nonlinear mapping onto the principal components of kernel principal componentanalysis (KPCA).
67
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.
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