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
Hyperspectral anomaly detection using kernel RX-algorithm
Heesung Kwon,Nasser M. Nasrabadi +1 more
- 24 Oct 2004
TL;DR: A nonlinear version of the well-known anomaly detection method, referred to as the RX-algorithm, is presented by extending this algorithm in a feature space associated with the original input space via a certain nonlinear mapping function.
16
fMRI based computer aided diagnosis of schizophrenia using fuzzy kernel feature extraction and hybrid feature selection
TL;DR: A three-phase dimension reduction that comprises of segmentation of voxels of 3-D spatial maps into anatomical brain regions; feature extraction from each region using a novel fuzzy kernel principal component analysis; and a novel hybrid (filter-cum-wrapper) feature selection for determining a reduced subset of discriminative features.
16
Classification and Quantitative Evaluation of Eddy Current Based on Kernel-PCA and ELM for Defects in Metal Component
Weiquan Deng,Bo Ye,Jun Bao,Huang Guoyong,Jiande Wu +4 more
- 01 Feb 2019
TL;DR: In this paper, the feature extraction of non-linear signals is carried out using the kernel-based principal component analysis (KPCA) algorithm and the classification of an extreme learning machine (ELM) for different defects is studied, which involves automatic defect classification and quantitative analysis.
16
•Posted Content
Disentangled Representation Learning and Generation with Manifold Optimization.
TL;DR: This work presents a representation learning framework that explicitly promotes disentanglement thanks to the combination of an auto-encoder with Principal Component Analysis (PCA) in latent space in the context of latent space models.
16
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