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
Linearized Kernel Dictionary Learning
Alona Golts,Michael Elad +1 more
TL;DR: A new approach of incorporating kernels into dictionary learning by approximate the kernel matrix using a cleverly sampled subset of its columns using the Nyström method, and decompose it by SVD to form new “virtual samples,” on which any linear dictionary learning can be employed.
81
Efficient approximate leave-one-out cross-validation for kernel logistic regression
G. Cawley,N. L. C. Talbot +1 more
TL;DR: This paper proposes an efficient approximate leave-one-out cross-validation method for kernel logistic regression, a binary classification method, to determine hyper-parameters and improve model selection, outperforming conventional k-fold cross-validation and Gaussian process classifiers on various benchmark datasets.
81
Hyperspectral Anomaly Detection Based on Machine Learning: An Overview
TL;DR: This review focuses on the HAD based on machine learning methods, which have witnessed remarkable progress in the recent years and can be grouped into the traditional machine learning and deep-learning-based methods.
81
Hyperspectral Anomaly Detection via Convolutional Neural Network and Low Rank With Density-Based Clustering
TL;DR: A novel AD algorithm based on convolutional neural network (CNN) and low-rank representation (LRR) and results show that the proposed method achieves a superior performance compared to some of the state-of-the-art methods in the field of hyperspectral AD.
80
Neighborhood Geometric Center Scaling Embedding for SAR ATR
TL;DR: A new approach to SAR image feature extraction that is named neighborhood geometric center scaling embedding, which is based on manifold learning theory is proposed, which has better recognition performance and higher stability than other methods.
80
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