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
Variable Metrics in Evolutionary Computation
Nikolaus Hansen
- 01 Jan 2009
TL;DR: An adaptive encoding procedure is presented, that is in principle applicable to any optimization procedure, and is proved to recover the covariance matrix adaptation evolution strategy (CMA-ES) when applied to a simple isotropic evolution strategy with step-size adaptation.
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Facial feature extraction by kernel independent component analysis
T. Martiriggiano,Marco Leo,Paolo Spagnolo,Tiziana D'Orazio +3 more
- 16 Sep 2005
TL;DR: Experimental results show that both kernel ICA and ICA representations are superior to representations based on PCA for recognizing faces across days and changes in expressions.
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•Dissertation
The spatial inductive bias of deep learning
Benjamin R. Mitchell
- 17 Mar 2017
TL;DR: A formal definition of how this type of spatial structure can be characterised is given, along with some statistical tools for testing whether spatial structure is present in a given dataset.
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Robust Speaker Identification Using Greedy Kernel PCA
Min-Seok Kim,IL-Ho Yang,Ha-Jin Yu +2 more
- 03 Nov 2008
TL;DR: A robust speaker identification system in noisy environments using greedy kernel principal component analysis, which can approximate kernel PCA with small representation error and outperforms conventional methods.
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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