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
Towards Automatically-Tuned Deep Neural Networks.
Hector Mendoza,Aaron Klein,Matthias Feurer,Jost Tobias Springenberg,Matthias Urban,Michael Burkart,Maximilian Dippel,Marius Lindauer,Frank Hutter +8 more
- 01 Jan 2019
TL;DR: Two versions of Auto-Net are presented, which provide automatically-tuned deep neural networks without any human intervention, and empirical results show that ensembling Auto- Net 1.0 with Auto-sklearn can perform better than either approach alone, and that Auto- net 2.0 can perform even better yet.
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Soft Sensor Modeling of Nonlinear Industrial Processes Based on Weighted Probabilistic Projection Regression
TL;DR: A novel weighted PPCR (WPPCR) algorithm is proposed in this paper for soft sensing of nonlinear processes and its effectiveness and flexibility are validated on a numerical example and an industrial process.
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The kernel-based nonlinear multivariate grey model
Xin Ma,Xin Ma,Zhibin Liu +2 more
TL;DR: This paper introduces a novel nonlinear multivariate grey model which is based on the kernel method, and named as the kernel-based GM(1, n), abbreviated as the KGM( 1, n).
111
Learning parametric dynamic movement primitives from multiple demonstrations
TL;DR: This paper proposes a novel approach to learn highly scalable CPs of basis movement skills from multiple demonstrations that allow the synthesis of novel movements with novel motion styles by specifying the linear coefficients of the bases as parameter vectors without losing useful properties of the DMPs.
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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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