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
Enter the Matrix: Factorization Uncovers Knowledge from Omics
Genevieve Stein-O’Brien,Raman Arora,Aedín C. Culhane,Alexander V. Favorov,Lana X. Garmire,Casey S. Greene,Loyal A. Goff,Yifeng Li,Aloune Ngom,Michael F. Ochs,Yanxun Xu,Elana J. Fertig +11 more
TL;DR: Matrix factorization (MF) techniques can reveal low-dimensional structure from high-dimensional data that reflect these interactions as discussed by the authors, which can uncover new biological knowledge from diverse high-throughput omics data in applications ranging from pathway discovery to timecourse analysis.
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Topology Identification and Learning over Graphs: Accounting for Nonlinearities and Dynamics
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TL;DR: The main goal of this paper is to outline overarching advances, and develop a principled framework to capture nonlinearities through kernels, which are judiciously chosen from a preselected dictionary to optimally fit the data.
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TL;DR: The proposed relational autoencoder models are evaluated and the experimental results show that considering data relationships can generate more robust features which achieve lower construction loss and then lower error rate in further classification compared to the other variants of autoencoders.
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Heterogeneous Ensemble-Based Infill Criterion for Evolutionary Multiobjective Optimization of Expensive Problems
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216
The individual identification method of wireless device based on dimensionality reduction and machine learning
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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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