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
Evaluation and improvement of temporal robustness and transfer performance of surface soil moisture estimated by machine learning regression algorithms
Jiaxin Qian,Yang Jie,Weidong Sun,Lingli Zhao,Shi Lei,Chaoya Dang +5 more
TL;DR: This study evaluates the temporal robustness and transfer performance of six machine learning regression algorithms for surface soil moisture estimation, identifying radar incidence angle and multi-spectral data as key factors for accurate estimation, and proposes strategies to mitigate poor transfer performance.
7
•Journal Article
An improved ECG-derived respiration method using kernel principal component analysis
TL;DR: KPCA proves to outperform PCA in the extraction of a respiratory signal from single lead ECGs to improve the performance of EDR signals using kernel PCA.
Applications of Kernel Machines to Structured Data
J Eichhorn
- 05 Mar 2007
TL;DR: The development and adaptation of kernel functions for decoding of neural activity and for image categorisation and an application of support vector machines as one prominent example of kernel algorithms to the task of object categorisation are presented.
Maximum Margin Clustering with Multivariate Loss Function
Bin Zhao,James T. Kwok,Changshui Zhang +2 more
- 06 Dec 2009
TL;DR: This paper presents a simple but powerful extension of the maximum margin clustering algorithm that optimizes multivariate performance measure specifically defined for clustering, including Normalized Mutual In- formation, Rand Index and F-measure.
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