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2015 | 52 | 2 | 55-74
Tytuł artykułu

Directional representation of data in Linear Discriminant Analysis

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
52
Numer
2
Strony
55-74
Opis fizyczny
Daty
wydano
2015-12-01
online
2015-12-12
Twórcy
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland, grala@amu.edu.pl
Bibliografia
  • 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.
  • Duchene L. (1987): A New Form of Discriminant Surfaces Using Polar Coordinates. Pattern Recognition 20(4): 437- 442.[Crossref]
  • 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]
  • Everitt B.S., Landau S., Leese M., Stahl D. (2011): Cluster Analysis. Wiley.
  • Hartigan J.A. (1975) Clustering Algorithms. New York, Wiley.
  • http://ics.uci.edu/~mlearn/MLRepository.html (UCI Machine Learning Repository)
  • Krzyśko M., Wołyński W., Górecki T., Skorzybut M. (2008): Systemy uczące się. Rozpoznawanie wzorców, analiza skupień i redukcja wymiarowości, WNT, Warsaw. (In Polish)
  • Matsushima T., Marcus P.S. (1995): A Spectral Method for Polar Coordinates. Journal of Computational Physics 120: 365-374.
  • Mardia K.V. (1972): Statistics of Directional Data. Academic Press, London.
  • Mardia K.V., Jupp P.E. (2000): Directional Statistics. Wiley Series in Probability and Statistics.
  • Rencher A.C., Christensen W.F. (2012): Methods of Multivariate Analysis, Third Edition. Wiley.
  • 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.
  • Shawe-Taylor J., Cristianini N. (2004): Kernel Methods for Pattern Analysis. Cambridge University Press.
  • Trendafilov N.T. (2013): From simple structure to sparse components: a review. Comput. Stat. (Online first article) 10.1007/500180-013-0434-5
  • 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).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_bile-2015-0006
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