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
Domain Generalization Based on Transfer Component Analysis
Thomas Grubinger,Adriana Birlutiu,Holger Schöner,Thomas Natschläger,Tom Heskes +4 more
- 10 Jun 2015
TL;DR: Experimental results demonstrate that Multi-TCA can improve predictive performance on previously unseen domains and is proposed as an extension of TCA to multiple domains as well as Multi-SSTCA, which is an extension to TCA for semi-supervised learning.
38
Face Recognition from Face Motion Manifolds using Robust Kernel Resistor-Average Distance
Ognjen Arandjelovic,Roberto Cipolla +1 more
- 27 Jun 2004
TL;DR: A kernel-based algorithm is introduced that retains the simplicity of the closed-form expression for the RAD between two normal distributions, while allowing for modelling of complex, nonlinear manifolds and how errors in the face registration process can be modelled to significantly improve recognition.
Constructing facial identity surfaces in a nonlinear discriminating space
Yongmin Li,Shaogang Gong,Heather M. Liddell +2 more
- 08 Dec 2001
TL;DR: Kernel Discriminant Analysis is developed to extract the significant non-linear discriminating features which maximise the between- class variance and minimise the within-class variance in multi-view face images.
Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method.
TL;DR: An efficient two‐stage Monte Carlo approach for small failure probability analysis in high‐dimensional groundwater contaminant transport modeling is proposed and is shown to be 100 times faster than the traditional MC approach in achieving the same level of estimation accuracy.
37
Exploring the Linear Subspace Hypothesis in Gender Bias Mitigation
Francisco Vargas,Ryan Cotterell +1 more
- 01 Nov 2020
TL;DR: This work takes inspiration from kernel principal component analysis and derive a non-linear bias isolation technique and shows that gender bias is in fact well captured by a linear subspace, justifying the assumption of Bolukbasi et al. (2016).
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