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
Nuclear accident source term estimation using Kernel Principal Component Analysis, Particle Swarm Optimization, and Backpropagation Neural Networks
Yongsheng Ling,Yongsheng Ling,Qi Yue,Chai Chaojun,Qing Shan,Daqian Hei,Wenbao Jia,Wenbao Jia +7 more
TL;DR: The proposed source term estimation method, based on the Backpropagation Neural Network, can estimate the release rate of I-131 after half an hour of release, which is helpful to the emergency response, or provide an initial value or priori information for other methods.
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KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization
TL;DR: Comprehensive experiments on widely used public datasets show that KCRC-LCD is a robust discriminative classifier with both excellent performance and good scalability, being comparable or outperforming many other state-of-the-art approaches.
Unsupervised State-Space Modeling Using Reproducing Kernels
TL;DR: This work proposes a novel framework for the design of state-space models (SSMs) whereby the state-transition function of the model is parametrized using reproducing kernels and shows that the proposed algorithm outperforms kernel adaptive filters in the prediction of real-world time series, while also providing probabilistic estimates, a key advantage over standard methods.
34
Face recognition for look-alikes: A preliminary study
TL;DR: The analysis shows that neither humans nor automatic face recognition algorithms are efficient in recognizing look-alikes, and an algorithm is proposed to improve the face verification accuracy.
33
Face Recognition Based on Videos by Using Convex Hulls
TL;DR: New video-based classification methods designed for reducing the required disk space of data samples and speed up the testing process in large-scale face recognition systems are introduced.
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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