On Feature Extraction via Kernels

Using the kernel trick idea and the kernels-as-features idea, we can construct two kinds of nonlinear feature spaces, where linear feature extraction algorithms can be employed to extract nonlinear features. In this correspondence, we study the relationship between the two kernel ideas applied to ce...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2008-04, Vol.38 (2), p.553-557
Main Authors: Yang, Cheng, Wang, Liwei, Feng, Jufu
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Artificial Intelligence
Canonical correlation analysis (CCA)
Computer Simulation
Cybernetics
Data Interpretation, Statistical
Discriminant Analysis
Equivalence
Feature extraction
Information Storage and Retrieval - methods
Kernel
kernel trick
Kernels
kernels as features
Law
Learning systems
Legal factors
Linear discriminant analysis
linear discriminant analysis (LDA)
Machine intelligence
Models, Statistical
nonlinear feature extraction
Nonlinearity
Pattern Recognition, Automated - methods
Principal Component Analysis
principal component analysis (PCA)
scaling
Support vector machines
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Description
Summary:Using the kernel trick idea and the kernels-as-features idea, we can construct two kinds of nonlinear feature spaces, where linear feature extraction algorithms can be employed to extract nonlinear features. In this correspondence, we study the relationship between the two kernel ideas applied to certain feature extraction algorithms such as linear discriminant analysis, principal component analysis, and canonical correlation analysis. We provide a rigorous theoretical analysis and show that they are equivalent up to different scalings on each feature. These results provide a better understanding of the kernel method.
ISSN:1083-4419
2168-2267
1941-0492
2168-2275
DOI:10.1109/TSMCB.2007.913604