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
Advances in kernel methods: support vector learning
Bernhard Schölkopf,Christopher John Burges,Alexander J. Smola +2 more
- 08 Feb 1999
TL;DR: Support vector machines for dynamic reconstruction of a chaotic system, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel.
7.3K
Williamson, estimating the support of a high-dimensional distribution
Bernhard Schölkopf,John Platt,J Shawe Taylor +2 more
- 01 Jan 2001
TL;DR: The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data by carrying out sequential optimization over pairs of input patterns and providing a theoretical analysis of the statistical performance of the algorithm.
5K
From frequency to meaning: vector space models of semantics
Peter D. Turney,Patrick Pantel +1 more
TL;DR: The goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs, and to provide pointers into the literature for those who are less familiar with the field.
•Proceedings Article
Support Vector Method for Novelty Detection
Bernhard Schölkopf,Robert C. Williamson,Alexander J. Smola,John Shawe-Taylor,John Platt +4 more
- 29 Nov 1999
TL;DR: The algorithm is a natural extension of the support vector algorithm to the case of unlabelled data and is regularized by controlling the length of the weight vector in an associated feature space.
Iterative Quantization: A Procrustean Approach to Learning Binary Codes for Large-Scale Image Retrieval
TL;DR: This paper addresses the problem of learning similarity-preserving binary codes for efficient similarity search in large-scale image collections by proposing a simple and efficient alternating minimization algorithm, dubbed iterative quantization (ITQ), and demonstrating an application of ITQ to learning binary attributes or "classemes" on the ImageNet data set.
2.1K
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