Directional representation of data in Linear Discriminant Analysis

Jolanta Grala-Michalak

Biometrical Letters (2015)

  • Volume: 52, Issue: 2, page 55-74
  • ISSN: 1896-3811

Abstract

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Sometimes feature representations of measured individuals are better described by spherical coordinates than Cartesian ones. The author proposes to introduce a preprocessing step in LDA based on the arctangent transformation of spherical coordinates. This nonlinear transformation does not change the dimension of the data, but in combination with LDA it leads to a dimension reduction if the raw data are not linearly separated. The method is presented using various examples of real and artificial data.

How to cite

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Jolanta Grala-Michalak. "Directional representation of data in Linear Discriminant Analysis." Biometrical Letters 52.2 (2015): 55-74. <http://eudml.org/doc/275953>.

@article{JolantaGrala2015,
abstract = {Sometimes feature representations of measured individuals are better described by spherical coordinates than Cartesian ones. The author proposes to introduce a preprocessing step in LDA based on the arctangent transformation of spherical coordinates. This nonlinear transformation does not change the dimension of the data, but in combination with LDA it leads to a dimension reduction if the raw data are not linearly separated. The method is presented using various examples of real and artificial data.},
author = {Jolanta Grala-Michalak},
journal = {Biometrical Letters},
keywords = {LDA; pattern recognition; spherical coordinates; dimension reduction; PCA; directional statistics},
language = {eng},
number = {2},
pages = {55-74},
title = {Directional representation of data in Linear Discriminant Analysis},
url = {http://eudml.org/doc/275953},
volume = {52},
year = {2015},
}

TY - JOUR
AU - Jolanta Grala-Michalak
TI - Directional representation of data in Linear Discriminant Analysis
JO - Biometrical Letters
PY - 2015
VL - 52
IS - 2
SP - 55
EP - 74
AB - Sometimes feature representations of measured individuals are better described by spherical coordinates than Cartesian ones. The author proposes to introduce a preprocessing step in LDA based on the arctangent transformation of spherical coordinates. This nonlinear transformation does not change the dimension of the data, but in combination with LDA it leads to a dimension reduction if the raw data are not linearly separated. The method is presented using various examples of real and artificial data.
LA - eng
KW - LDA; pattern recognition; spherical coordinates; dimension reduction; PCA; directional statistics
UR - http://eudml.org/doc/275953
ER -

References

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  1. Aeberhard S., Coomans D., de Vel O. (1992): The performance of statistical pattern recognition methods in high dimensional settings. Tech. Rep. No 92-02, Dept. Of Computer Science and Depth. Of Mathematics and Statistics, James Cook University of North Queensland. Zbl0968.68204
  2. Duchene L. (1987): A New Form of Discriminant Surfaces Using Polar Coordinates. Pattern Recognition 20(4): 437- 442.[Crossref] 
  3. Duchene L., Leclerq S. (1988): An Optimal Transformation for Discriminant and Principal Component Analysis. IEEE Trans. Pattern Analysis and Machine Intelligence 10(6): 978-983.[Crossref][WoS] Zbl0655.62064
  4. Everitt B.S., Landau S., Leese M., Stahl D. (2011): Cluster Analysis. Wiley. 
  5. Hartigan J.A. (1975) Clustering Algorithms. New York, Wiley. Zbl0372.62040
  6. http://ics.uci.edu/~mlearn/MLRepository.html (UCI Machine Learning Repository) 
  7. Krzyśko M., Wołyński W., Górecki T., Skorzybut M. (2008): Systemy uczące się. Rozpoznawanie wzorców, analiza skupień i redukcja wymiarowości, WNT, Warsaw. (In Polish) 
  8. Matsushima T., Marcus P.S. (1995): A Spectral Method for Polar Coordinates. Journal of Computational Physics 120: 365-374. Zbl0842.65051
  9. Mardia K.V. (1972): Statistics of Directional Data. Academic Press, London. Zbl0244.62005
  10. Mardia K.V., Jupp P.E. (2000): Directional Statistics. Wiley Series in Probability and Statistics. Zbl0935.62065
  11. Rencher A.C., Christensen W.F. (2012): Methods of Multivariate Analysis, Third Edition. Wiley. Zbl1275.62011
  12. Sajjanhar A., Lu G., Zhang D. (2007): A Composite Descriptor for Shape Retrieval. Proceedings of the 6th IEEE/ACIS International Conference on Computer and Information Science, IEEE Computer Society, Melbourne, Australia: 795-800. 
  13. Shawe-Taylor J., Cristianini N. (2004): Kernel Methods for Pattern Analysis. Cambridge University Press. Zbl0994.68074
  14. Trendafilov N.T. (2013): From simple structure to sparse components: a review. Comput. Stat. (Online first article) 10.1007/500180-013-0434-5 
  15. Xiong T., Ye J., Cherkassky V. (2006): Kernel Uncorrelated and Orthogonal Discriminant Analysis: A Unified Approach. Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’06). 

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