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
Kernel Trick for the Cross-Section
TL;DR: This work proposes a method which uses economically-driven regularization to construct a stochastic discount factor (SDF) when the set of characteristics is extended to an arbitrary set of non-linear functions of original characteristics, and borrows ideas from a machine learning technique known as the "kernel trick" to circumvent the curse of dimensionality.
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A just-in-time modeling approach for multimode soft sensor based on Gaussian mixture variational autoencoder
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TL;DR: In this article, a soft sensor model based on Gaussian mixture variational autoencoder (GMVAE) under the just-in-time learning (JITL) framework was developed.
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Kernel Methods for Accurate UWB-Based Ranging With Reduced Complexity
TL;DR: In this paper, a range estimation method based on kernel principal component analysis (kPCA) is proposed for the UWB channel impulse response, in which the selected channel parameters are projected onto a nonlinear orthogonal high-dimensional space, and a subset of these projections is then used as an input for ranging.
Discriminant Absorption-Feature Learning for Material Classification
Zhouyu Fu,Antonio Robles-Kelly +1 more
TL;DR: A novel approach to object-material identification in spectral imaging is developed by combining the use of invariant spectral absorption features and statistical machine-learning techniques to robustly recover those bands that are most relevant to the identification process.
A new active learning strategy for soft sensor modeling based on feature reconstruction and uncertainty evaluation
Qi-feng Tang,Dewei Li,Yugeng Xi +2 more
TL;DR: A novel active learning (AL) strategy is proposed to reduce the labeling cost, which iteratively select the most informative candidates by jointly evaluating two criteria: representativeness and uncertainty.
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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