A kernel-based learning algorithm combining kernel discriminant coordinates and kernel principal components

Karol Deręgowski; Mirosław Krzyśko

Biometrical Letters (2014)

  • Volume: 51, Issue: 1, page 57-73
  • ISSN: 1896-3811

Abstract

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Kernel principal components (KPC) and kernel discriminant coordinates (KDC), which are the extensions of principal components and discriminant coordinates, respectively, from a linear domain to a nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. The kernel discriminant coordinates space has proven to be a very powerful space for pattern recognition. However, further study shows that there are still drawbacks in this method. To improve the performance of pattern recognition, we propose a new learning algorithm combining the advantages of KPC and KDC

How to cite

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Karol Deręgowski, and Mirosław Krzyśko. "A kernel-based learning algorithm combining kernel discriminant coordinates and kernel principal components." Biometrical Letters 51.1 (2014): 57-73. <http://eudml.org/doc/268832>.

@article{KarolDeręgowski2014,
abstract = {Kernel principal components (KPC) and kernel discriminant coordinates (KDC), which are the extensions of principal components and discriminant coordinates, respectively, from a linear domain to a nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. The kernel discriminant coordinates space has proven to be a very powerful space for pattern recognition. However, further study shows that there are still drawbacks in this method. To improve the performance of pattern recognition, we propose a new learning algorithm combining the advantages of KPC and KDC},
author = {Karol Deręgowski, Mirosław Krzyśko},
journal = {Biometrical Letters},
keywords = {kernel principal components; kernel discriminant coordinates},
language = {eng},
number = {1},
pages = {57-73},
title = {A kernel-based learning algorithm combining kernel discriminant coordinates and kernel principal components},
url = {http://eudml.org/doc/268832},
volume = {51},
year = {2014},
}

TY - JOUR
AU - Karol Deręgowski
AU - Mirosław Krzyśko
TI - A kernel-based learning algorithm combining kernel discriminant coordinates and kernel principal components
JO - Biometrical Letters
PY - 2014
VL - 51
IS - 1
SP - 57
EP - 73
AB - Kernel principal components (KPC) and kernel discriminant coordinates (KDC), which are the extensions of principal components and discriminant coordinates, respectively, from a linear domain to a nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. The kernel discriminant coordinates space has proven to be a very powerful space for pattern recognition. However, further study shows that there are still drawbacks in this method. To improve the performance of pattern recognition, we propose a new learning algorithm combining the advantages of KPC and KDC
LA - eng
KW - kernel principal components; kernel discriminant coordinates
UR - http://eudml.org/doc/268832
ER -

References

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  3. Bache K., Lichman M. (2013): UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science. 
  4. Fisher R.A. (1936): The use of multiple measurements in taxonomic problem. Annals of Eugenics 7: 179-188. 
  5. Friedman J.H. (1989): Regularized discriminant analysis. Journal of the American Statistical Association 84: 165-175. 
  6. Hotelling H. (1933): Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology 24: 417-441, 498-520. Zbl59.1182.04
  7. Mika S., Rätsch G., Weston J., Schölkopf B., Müller K.R. (1999): Fisher discriminant analysis with kernels. In Y.H. Hu, J. Larsen, E. Wilson, and S. Douglas (eds.), Neural Networks for Signal Processing IV: 41-48. 
  8. Schölkopf B., Smola A., Müller K.B. (1998): Nonlinear component analysis as a kernel eigenvalues problem. Neural Computation 10: 1299-1319.[WoS] 
  9. Seber G.A.F. (1984): Multivariate Observations. Wiley, New York. 
  10. Shawe-Taylor J., Cristianini N. (2004): Kernel methods for pattern analysis. Cambridge University Press, Cambridge, UK. Zbl0994.68074

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