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
Malignant nodule detection on lung CT scan images with kernel RX-algorithm
Aminmohammad Roozgard,Samuel Cheng,Hong Liu +2 more
- 08 Jun 2012
TL;DR: The preliminary results of applying the kernel RX-algorithm on annotated public access databases suggests that the proposed method may provide a means for early detection of the malignant nodules.
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Visual Analytics of Multidimensional Projections for Constructing Classifier Decision Boundary Maps
Mateus Espadoto,Francisco Caio M. Rodrigues,Alexandru Telea +2 more
- 25 Feb 2019
TL;DR: This work designs and performs a detailed study aimed at finding the best DR techniques to use when creating trustworthy dense maps, by studying a large collection of 28 DR algorithms, 4 classifiers, and 2 datasets from a real-world challenging classification problem.
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Damage quantification using transfer component analysis combined with Gaussian process regression
TL;DR: The use of transfer component analysis is proposed to mitigate divergences between the model/structure’s features, and the label consistency requirement is applied in combination with a Gaussian process regression model for damage quantification.
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Patent
Computerized cluster analysis framework for decorrelated cluster identification in datasets
Patrick Hall,Ilknur Kaynar Kabul,Jared Langford Dean,Ralph Abbey,Susan Haller,Jorge Silva +5 more
- 02 Dec 2014
TL;DR: In this paper, a computing device is provided to automatically cluster a dataset and each data point of the plurality of data points is associated with a variable to define a plurality of variables.
15
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