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
Constructing Facial Identity Surfaces for Recognition
TL;DR: A novel approach to face recognition is presented by constructing facial identity structures across views and over time, referred to as identity surfaces, in a Kernel Discriminant Analysis (KDA) feature space, aimed at addressing three challenging problems in face recognition.
On the influence of over-parameterization in manifold based surrogates and deep neural operators
TL;DR: In this paper , the authors compare manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and examine the effect of over-parameterization on generalization.
Learning over Sets using Boosted Manifold Principal Angles (BoMPA)
Tae-Kyun Kim,Ognjen Arandjelovic,Roberto Cipolla +2 more
- 01 Jan 2005
TL;DR: The proposed method based on comparisons between corresponding vector subspaces is shown to outperform state-of-the-art methods in the literature and to demonstrate how boosting can be used for application-optimal principal angle fusion.
High-Dimensional Potential Energy Surfaces for Molecular Simulations
TL;DR: An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given, including empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, and neural network-learned representations and combinations thereof.
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Robot arm pose estimation by pixel-wise regression of joint angles
Felix Widmaier,Daniel Kappler,Stefan Schaal,Jeannette Bohg +3 more
- 16 May 2016
TL;DR: This work proposes an approach for robot arm pose estimation that uses depth images of the arm as input to directly estimate angular joint positions and shows that this approach improves previous work both in terms of computational complexity and accuracy.
43
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