Geodesic
A learning algorithm combining functional discriminant coordinates and functional principal components
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 127-141.

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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.
Keywords: functional principal components, functional discriminant coordinates 
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Górecki, Tomasz; Krzyśko, Mirosław. A learning algorithm combining functional discriminant coordinates and functional principal components. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 127-141. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a8/

[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] 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] 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] 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.

[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] 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

[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

[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

[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] 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] 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

[12] J.O. Ramsay and B.W. Silverman, Functional Data Analysis, Second Edition (Springer, 2005). doi: 10.1007/b98888

[13] G.A.F. Seber, Multivariate Observations (Wiley, 1984). doi: 10.1002/9780470316641

[14] G. Shmueli, To explain or to predict? Statistical Science 25 (3) (2010) 289-310. doi: 10.1214/10-STS330

[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