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
Principal Direction Divisive Partitioning with Kernels and k-Means Steering
Dimitrios Zeimpekis,Efstratios Gallopoulos +1 more
- 01 Jan 2008
TL;DR: This work proposes, implements, and evaluates several schemes that combine partitioning and hierarchical algorithms, specifically k-means and principal direction divisive partitioning (PDDP), and suggests that it is advantageous to steer PDDP using k-Means.
15
Fault detection and diagnosis for non-linear processes empowered by dynamic neural networks
Georgios Gravanis,Ioannis Dragogias,Konstantinos Papakiriakos,Chrysovalantou Ziogou,Konstantinos I. Diamantaras +4 more
TL;DR: A Fault Detection and Diagnosis framework for Non-Linear Processes utilizing Dynamic Neural Networks and feature reduction methods is proposed and it is demonstrated that this method outperforms state of the art methods in the majority of those faults.
15
Learning motifs and their hierarchies in atomic resolution microscopy
15 Apr 2022
TL;DR: In this article , a machine learning framework was proposed to extract a hierarchy of complex structural motifs from atomically resolved images, and the motif hierarchies provided statistically grounded clues about the favored and frustrated pathways during self-assembly.
15
Redes neuronales y preprocesado de variables para modelos y sensores en bioingeniería
Fernando Mateo Jiménez
- 19 Jul 2012
TL;DR: The Tesis Doctoral as mentioned in this paper proposes an alternative to the aproximación of modelos and procesos in the ambito cientifico and, mas concretamente, en aplicaciones complejas de bio-informatia.
Automating X-ray Fluorescence Analysis for Rapid Astrobiology Surveys
David R. Thompson,David Flannery,Ravi Lanka,Abigail C. Allwood,Brian D. Bue,Benton C. Clark,W. Timothy Elam,Tara Estlin,Robert Hodyss,Joel A. Hurowitz,Yang Liu,Lawrence A. Wade +11 more
TL;DR: In this paper, the authors demonstrate operational approaches to overcome the bottlenecks by specialized early-stage science data processing, such as PIXL (Planetary Instrument for X-ray Lithochemistry) and SHERLOC (Scanning Habitable Environments with Raman Luminescence for Organics and Chemicals).
15
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