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.
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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.
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Citations
Kernel Grassmannian distances and discriminant analysis for face recognition from image sets
Tiesheng Wang,Pengfei Shi +1 more
TL;DR: This work addresses the problem of face recognition from image sets, where subject-specific subspaces instead of image vectors are compared, and shows that kernel Grassmannian distances in feature space can be implicitly computed from the input data.
89
Patent
Spectral kernels for learning machines
Nello Cristianini
- 01 Mar 2002
TL;DR: The spectral kernel machine as discussed by the authors combines kernel functions and spectral graph theory for solving problems of machine learning The data points in the dataset are placed in the form of a matrix known as a kernel matrix, or Gram matrix, containing all pairwise kernels between the data points.
89
Speaker Recognition With Session Variability Normalization Based on MLLR Adaptation Transforms
TL;DR: A new modeling approach for speaker recognition that uses the maximum-likelihood linear regression (MLLR) adaptation transforms employed by a speech recognition system as features for support vector machine (SVM) speaker models is presented.
88
Data visualization by nonlinear dimensionality reduction
Andrej Gisbrecht,Barbara Hammer +1 more
TL;DR: In this overview, commonly used dimensionality reduction techniques for data visualization and their properties are reviewed and the focus lies on an intuitive understanding of the underlying mathematical principles rather than detailed algorithmic pipelines.
88
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