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
Nonlinear Dimensionality Reduction for Discriminative Analytics of Multiple Datasets
TL;DR: This paper puts forth a novel approach, termed discriminative (d) PCA, for such discrim inative analytics of multiple datasets jointly, and under certain conditions, dPCA is proved to be least-squares optimal in recovering the latent subspace vector unique to the target data relative to background data.
30
Novel dimensionality reduction approach for unsupervised learning on small datasets
TL;DR: This work focuses on an image classification task in which only several unlabeled images per class are available for learning and low computational complexity is required, and finds that the F-transform is the most suitable method to solve the task.
30
A cellular automata model based on nonlinear kernel principal component analysis for urban growth simulation
Yongjiu Feng,Yan Liu +1 more
TL;DR: In this paper, a cellular automata (CA) model based on nonlinear kernel principal component analysis (KPCA) is presented to simulate the spatiotemporal process of urban growth.
30
Supervised feature selection by constituting a basis for the original space of features and matrix factorization
TL;DR: The experimental results show that the proposed SFS-BMF method outperforms some state-of-the-art feature selection methods with respect to classification performance and also according to the computational complexity.
30
Color Orchestra: Ordering Color Palettes for Interpolation and Prediction
TL;DR: Zhang et al. as mentioned in this paper proposed a divide-and-conquer sorting algorithm to rearrange the colors in the palettes in a coherent order, which allows meaningful interpolation between color palettes.
30
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