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 PCA-based GLRT for nonlinear fault detection of chemical processes
TL;DR: In this paper, a nonlinear statistical fault detection using kernel principal component analysis (KPCA)-based generalized likelihood ratio test (GLRT) is proposed, which is used to detect single as well as multiple sensor faults.
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Feature Selection and Extraction
Shigeo Abe
- 01 Jan 2010
TL;DR: Conventional classifiers do not have a mechanism to control class boundaries, so if the number of features, i.e., input variables, is large compared to the number-of-training data, class boundaries may not overlap.
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•Proceedings Article
Online cross-modal hashing for web image retrieval
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- 12 Feb 2016
TL;DR: This paper proposes Online Cross-modal Hashing (OCMH) which can effectively address the above two problems by learning the shared latent codes (SLC) of hash codes and dynamic transfer matrix, and demonstrates the effectiveness and efficiency of OCMH for online cross- modal web image retrieval.
Dimensionality Reduction Via Graph Structure Learning
Qi Mao,Li Wang,Steve Goodison,Yijun Sun +3 more
- 10 Aug 2015
TL;DR: A new dimensionality-reduction framework that involves the learning of a mapping function that projects data points in the original high-dimensional space to latent points in a low- dimensional space that are then used directly to construct a graph.
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MnM: a Max/MSP mapping toolbox
Frédéric Bevilacqua,Rémy Muller,Norbert Schnell +2 more
- 01 May 2005
TL;DR: This report describes the development on the Max/MSP toolbox MnM dedicated to mapping between gesture and sound, and more generally to statistical and machine learning methods.
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.
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