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

Access Full Article

top

 Access to full text

 Full (PDF)

Abstract

top

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

top

• MLA
• BibTeX
• RIS

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

top

1. Aronszajn N. (1950): Theory of reproducing kernels. Transactions of the American Mathematical Society 68: 337-404. Zbl0037.20701
2. Badat G., Anouar F. (2000): Generalized discriminant analysis using a kernel approach. Neural Computation 12: 2385-2404. 
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

Citations in EuDML Documents

top

1. Bogna Zawieja, Katarzyna Kaźmierczak, Allocation of oaks to Kraft classes based on linear and nonlinear kernel discriminant variables

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget. български (bg) čeština (cs) Deutsch (de) ελληνικά (el) English (en) español (es) français (fr) italiano (it) lietuvių kalba (lt) polski (pl) português (pt) română (ro) русский (ru) slovenčina (sk)

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page 5 10 15 20

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.

OK