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
Visualization Framework for High-Dimensional Spatio-Temporal Hydrological Gridded Datasets using Machine-Learning Techniques
TL;DR: A generic workflow to project high-dimensional spatio-temporal data on a two-dimensional (2D) plane accurately and compare dimensionality reduction techniques (DRTs) in terms of resolution and computational efficiency to represent 2D projection spatially using a 2D perceptually uniform background color map is presented.
22
Sparse Passive-Aggressive Learning for Bounded Online Kernel Methods
TL;DR: This article proposes a novel framework for bounded online kernel methods, named “Sparse Passive-Aggressive (SPA)” learning, which is able to yield a final output kernel-based hypothesis with a bounded number of support vectors, and theoretically proves that SPA achieves an optimal mistake bound in expectation, and empirically shows that it outperforms various budget online kernel learning algorithms.
22
Unsupervised Large Margin Discriminative Projection
TL;DR: A new dimensionality reduction method called maximum margin projection (MMP), which aims to project data samples into the most discriminative subspace, where clusters are most well-separated, and shows that the computation time needed for MMP can be treated as linear in the dataset size.
22
Video representation and coding using a sparse steered mixture-of-experts network
Lieven Lange,Ruben Verhack,Thomas Sikora +2 more
- 01 Jan 2016
TL;DR: A novel approach for video compression that explores spatial as well as temporal redundancies over sequences of many frames in a unified framework and developed a sparse Steered Mixture-of-Experts (SMoE) regression network for coding video in the pixel domain.
21
An unsupervised approach for health index building and for similarity-based remaining useful life estimation
TL;DR: In this article , an automatic and unsupervised approach based on the Kernel Principal Component Analysis (KPCA) is proposed to enhance the Health Index creation. But, it does not have the capability to estimate the remaining useful life (RUL).
21
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