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
EGD-SNet: A computational search engine for predicting an end-to-end machine learning pipeline for Energy Generation & Demand Forecasting
Faiza Mehmood,Muhammad U. Ghani,Hina Ghafoor,Rehab Shahzadi,Muhammad Nabeel Asim,Waqar Mahmood +5 more
TL;DR: In this article , an end-to-end framework named Energy Generation and Demand forecasting Search Net (EGD-SNet) is presented, which is capable of predicting energy generation, demand and temperature in multiple regions.
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Subclass Graph Embedding and a Marginal Fisher Analysis paradigm
TL;DR: A novel DR algorithm, which uses subclass discriminant information, called Subclass Marginal Fisher Analysis (SMFA) has been proposed and it is shown that SMFA outperforms in most of the cases the state-of-the-art demonstrating the efficacy and power of SGE as a platform to develop new methods.
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Linear programming approaches for multicategory support vector machines
TL;DR: It is shown that any data points nonlinearly, and implicitly, projected into the feature space by kernel functions can be approximately expressed as points lying a low dimensional Euclidean space explicitly, which enables to develop linear programming formulations for nonlinear discriminators.
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Simple and Efficient Speaker Comparison using Approximate KL Divergence
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TL;DR: A new approximate KL divergence distance extending earlier GMM parameter vector SVM kernels is used and a weighted nuisance projection method for channel compensation is applied, and a simple eigenvector method of training is presented.
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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.
2.6K