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
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TL;DR: A novel method to represent the dMRI more sparsely using self-learned nonlinear dictionaries based on kernel methods and a new iterative approach for image reconstruction relying on pre-image reconstruction is developed within CS framework.
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Human face recognition based on ensemble of polyharmonic extreme learning machine
TL;DR: Comparison experiments of the proposed classifier with some other state-of-the-art approaches for human face recognition have been carried out on five well-known face databases, and the experimental results show that the proposed method can achieve higher recognition rate.
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A novel kernel collaborative representation approach for image classification
Weiyang Liu,Lijia Lu,Hui Li,Wei Wang,Yuexian Zou +4 more
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Visual Data Mining and Machine Learning.
Fabrice Rossi
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Data-dependent compression of random features for large-scale kernel approximation
Raj Agrawal,Trevor Campbell,Jonathan H. Huggins,Tamara Broderick +3 more
- 11 Apr 2019
TL;DR: This work proposes to combine the simplicity and generality of RFMs with a data-dependent feature selection scheme to achieve desirable theoretical approximation properties of Nystrom with just O(log J+) features, and shows that the method achieves small kernel matrix approximation error and better test set accuracy with provably fewer random features than state-of-the-art methods.
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