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
Kernel principal components are maximum entropy projections
Antonio R. C. Paiva,Jian-Wu Xu,Jose C. Principe +2 more
- 05 Mar 2006
TL;DR: It is proved that Kernel PCA provides optimum entropy projections in the input space when the Gaussian kernel is used for the mapping and a sample estimate of Renyi’s entropy based on the Parzen window method is employed.
A spectral method for assessing and combining multiple data visualizations
Rong Ma,Eric D. Sun,James Zou +2 more
TL;DR: In this article , a spectral method for assessing and combining multiple visualizations of a given dataset produced by diverse algorithms is proposed, which provides a quantitative measure -the visualization eigenscore -of the relative performance of the visualizations for preserving the structure around each data point.
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Autoencoding any Data through Kernel Autoencoders
TL;DR: The Kernel Autoencoder (KAE) as discussed by the authors is an extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, allowing to autoencode any kind of data by choosing X to be itself a RKHS.
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Maximally Correlated Principal Component Analysis Based on Deep Parameterization Learning
TL;DR: A novel dimensionality reduction model called maximally correlated PCA based on deep parameterization learning (MCPCADP), which takes nonlinear correlation into account in thedeep parameterization framework for the purpose of dimensionality reduce is proposed.
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A Line Complex-Based Evolutionary Algorithm for Many-Objective Optimization
TL;DR: Zhang et al. as discussed by the authors proposed to evolve solutions through line complex rather than solution points in Euclidean space, where Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum vectors.
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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.
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