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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
An MR brain images classification technique via the Gaussian radial basis kernel and SVM
Syrine Neffati,Okba Taouali +1 more
- 01 Dec 2017
TL;DR: A new 3D magnetic resonance head images (MRI) classifier based on KPCA and SVM is presented and it was observed that the proposed work outperforms other algorithms working on the same dataset in terms of accuracy, sensitivity and specificity.
19
Artificial intelligence in agriculture
Xanthoula Eirini Pantazi,Dimitrios Moshou,Dionysis Bochtis +2 more
- 01 Jan 2020
TL;DR: This chapter provides a detailed description regarding the scientific background of One Class Classification, One Class Support Vector Machines Hierarchical Self Organizing Maps and Active learning algorithms and their application in the field of Precision Agriculture.
19
Handwritten Chinese character recognition using nonlinear active shape models and the Viterbi algorithm
TL;DR: In this paper, radical extraction is carried out by nonlinear active shape models, in which kernel principal component analysis is employed to capture the nonlinear variation.
19
loopUI-0.1: indicators to support needs and practices in 3D geological modelling uncertainty quantification
TL;DR: A Python package called loopUI-0.1 is proposed that provides a set of local and global indicators to measure uncertainty and features dissimilarities among an ensemble of voxet models to support the needs of practitioners regarding 3D geological modelling and uncertainty quantification in the field.
Case-Based Retrieval Framework for Gene Expression Data
TL;DR: A case-based retrieval framework that uses a k-nearest-neighbor classifier with a weighted-feature-based similarity to retrieve previously treated patients based on their gene expression profiles for better diagnosis and treatment of childhood leukemia is proposed.
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