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
A Multi-Step Nonlinear Dimension-Reduction Approach with Applications to Big Data
TL;DR: In this paper, a dimension-reduction approach is presented to overcome challenges such as nonlinear relationships, heterogeneity, and noisy dimensions, where the data are first organized into random groups and each group is independently mapped into a low dimensional space via a parametric mapping.
Segmentation and Normalization of Human Ears Using Cascaded Pose Regression
Anika Pflug,Christoph Busch +1 more
- 15 Oct 2014
TL;DR: This research community has come up with a variety of feature extraction methods that are capable of handling occlusions and blur, however, these methods require the images to be geometrically normalized, which is mostly done manually at the moment.
Local proper generalized decomposition
Alberto Badías,David González,Icíar Alfaro,Francisco Chinesta,Elías Cueto +4 more
- 16 Oct 2017
TL;DR: In this article, three strategies for estimating the appropriate size of the local sub-domains where afterwards local PGD (l-PGD) is applied, which can be seen as a sort of a priori manifold learning or non-linear dimensionality reduction technique.
Incipient fault detection and diagnosis of nonlinear industrial process with missing data
Miao Mou,Xiaoqiang Zhao +1 more
TL;DR: Wang et al. as mentioned in this paper proposed a Mixed Kernel function Dissimilarity Neighborhood Preserving Embedding (MKDNPE) method to detect and diagnose incipient nonlinear faults in industrial processes with missing data.
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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