A learning algorithm combining functional discriminant coordinates and functional principal components

Tomasz Górecki; Mirosław Krzyśko

Discussiones Mathematicae Probability and Statistics (2014)

  • Volume: 34, Issue: 1-2, page 127-141
  • ISSN: 1509-9423

Abstract

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A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.

How to cite

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Tomasz Górecki, and Mirosław Krzyśko. "A learning algorithm combining functional discriminant coordinates and functional principal components." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 127-141. <http://eudml.org/doc/270840>.

@article{TomaszGórecki2014,
abstract = {A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.},
author = {Tomasz Górecki, Mirosław Krzyśko},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {functional principal components; functional discriminant coordinates},
language = {eng},
number = {1-2},
pages = {127-141},
title = {A learning algorithm combining functional discriminant coordinates and functional principal components},
url = {http://eudml.org/doc/270840},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Tomasz Górecki
AU - Mirosław Krzyśko
TI - A learning algorithm combining functional discriminant coordinates and functional principal components
JO - Discussiones Mathematicae Probability and Statistics
PY - 2014
VL - 34
IS - 1-2
SP - 127
EP - 141
AB - A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.
LA - eng
KW - functional principal components; functional discriminant coordinates
UR - http://eudml.org/doc/270840
ER -

References

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  1. [1] G. Bergmann and G. Hommel, Improvements of general multiple test procedures for redundant systems of hypotheses, in: Multiple Hypotheses Testing, P. Bauer, G. Hommel, E. Sonnemann (Ed.), Springer (1988) 110-115. doi: 10.1007/978-3-642-52307-6_8 
  2. [2] D. Cozzolino, E. Restaino and A. Fassio, Discrimination of yerba mate (ilex paraguayensis st. hil.) samples according to their geographical origin by means of near infrared spectroscopy and multivariate analysis, Sensing and Instrumentation for Food Quality and Safety 4 (2002) 67-72. doi: 10.1007/s11694-010-9096-y 
  3. [3] R.A. Fisher, The use of multiple measurements in taxonomic problem, Annals of Eugenics 7 (1936) 179-188. doi: 10.1111/j.1469-1809.1936.tb02137.x 
  4. [4] S. Garcia and F. Herrera, An extension on 'statistical comparisons of classifiers over multiple data sets' for all pairwise comparisons, Journal of Machine Learning Research 9 (2008) 2677-2694. Zbl1225.68178
  5. [5] T. Górecki and M. Krzyśko, Functional Principal Components Analysis, in: Data analysis methods and its applications, J. Pociecha, R. Decker (Ed.), C.H. Beck (2012) 71-87. 
  6. [6] T. Górecki, M. Krzyśko and Ł. Waszak, Functional discriminant coordinates, Communication in Statistics - Theory and Methods 43 (5) (2014) 1013-1025. doi: 10.1080/03610926.2013.828074 Zbl06301871
  7. [7] H. Hotelling, Analysis of a complex of statistical variables into principal components, Journal of Educational Psychology 24 (1933) 417-441, 498-520. doi: 10.1037/h0071325 Zbl59.1182.04
  8. [8] R. Iman and J. Davenport, Approximations of the critical region of the freidman statistic, Communications in Statistics - Theory and Methods 9 (6) (1980) 571-595. doi: 10.1080/03610928008827904 Zbl0451.62061
  9. [9] E. Keogh, Q. Zhu, B. Hu, Y. Hao, X. Xi, L. Wei and C.A. Ratanamahatana, The UCR Time Series Classification/Clustering, Homepage, 2011. http://www.cs.ucr.edu/~eamonn/time_series_data/. 
  10. [10] N.K. Kwak, S.H. Kim, C.W. Lee and T.S. Choi, An application of linear programming discriminant analysis to classifying and predicting the symptomatic status of hiv/aids patients, Journal of Medical Systems 26 (5) (2002) 427-438. 
  11. [11] T.S. Lim, W.Y. Loh and Y.S. Shih, A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms, Machine Learning 40 (3) (2000) 203-228. doi: 10.1023/A:1007608224229 Zbl0969.68669
  12. [12] J.O. Ramsay and B.W. Silverman, Functional Data Analysis, Second Edition (Springer, 2005). doi: 10.1007/b98888 Zbl1079.62006
  13. [13] G.A.F. Seber, Multivariate Observations (Wiley, 1984). doi: 10.1002/9780470316641 
  14. [14] G. Shmueli, To explain or to predict? Statistical Science 25 (3) (2010) 289-310. doi: 10.1214/10-STS330 Zbl1329.62045
  15. [15] F. Song, D. Zhang, Q. Chen and J. Wang, Face recognition based on a novel linear discriminant criterion, Pattern Analysis and Applications 10 (2007) 165-174. doi: 10.1007/s10044-006-0057-3 

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