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
A Generalized Representer Theorem
Bernhard Schölkopf,Bernhard Schölkopf,Ralf Herbrich,Ralf Herbrich,Alexander J. Smola +4 more
- 16 Jul 2001
TL;DR: The result shows that a wide range of problems have optimal solutions that live in the finite dimensional span of the training examples mapped into feature space, thus enabling us to carry out kernel algorithms independent of the (potentially infinite) dimensionality of the feature space.
Deep Learning for Anomaly Detection: A Review
TL;DR: A comprehensive survey of deep anomaly detection with a comprehensive taxonomy is presented in this paper, covering advancements in 3 high-level categories and 11 fine-grained categories of the methods.
1.3K
Shortest-path kernels on graphs
Karsten M. Borgwardt,Hans-Peter Kriegel +1 more
- 27 Nov 2005
TL;DR: This work proposes graph kernels based on shortest paths, which are computable in polynomial time, retain expressivity and are still positive definite, and shows significantly higher classification accuracy than walk-based kernels.
WSABIE: scaling up to large vocabulary image annotation
Jason Weston,Samy Bengio,Nicolas Usunier +2 more
- 16 Jul 2011
TL;DR: This work proposes a strongly performing method that scales to image annotation datasets by simultaneously learning to optimize precision at the top of the ranked list of annotations for a given image and learning a low-dimensional joint embedding space for both images and annotations.
Principal component analysis: a method for determining the essential dynamics of proteins.
Charles David,Donald J. Jacobs +1 more
TL;DR: Best practices for applying standard PCA are reviewed, useful variants are described, why one may wish to make comparison studies, and a set of metrics that make comparisons possible are described.
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