Canonical correlation analysis for functional data
Mirosław Krzyśko; Łukasz Waszak
Biometrical Letters (2013)
- Volume: 50, Issue: 2, page 95-105
- ISSN: 1896-3811
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topMirosław Krzyśko, and Łukasz Waszak. "Canonical correlation analysis for functional data." Biometrical Letters 50.2 (2013): 95-105. <http://eudml.org/doc/268715>.
@article{MirosławKrzyśko2013,
abstract = {Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation, and is equivalent to solving a generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we propose a new method of constructing canonical correlations and canonical variables for a pair of stochastic processes represented by a finite number of orthonormal basis functions.},
author = {Mirosław Krzyśko, Łukasz Waszak},
journal = {Biometrical Letters},
keywords = {functional data; orthonormal basis; stochastic processes; canonical correlation analysis},
language = {eng},
number = {2},
pages = {95-105},
title = {Canonical correlation analysis for functional data},
url = {http://eudml.org/doc/268715},
volume = {50},
year = {2013},
}
TY - JOUR
AU - Mirosław Krzyśko
AU - Łukasz Waszak
TI - Canonical correlation analysis for functional data
JO - Biometrical Letters
PY - 2013
VL - 50
IS - 2
SP - 95
EP - 105
AB - Classical canonical correlation analysis seeks the associations between two data sets, i.e. it searches for linear combinations of the original variables having maximal correlation. Our task is to maximize this correlation, and is equivalent to solving a generalized eigenvalue problem. The maximal correlation coefficient (being a solution of this problem) is the first canonical correlation coefficient. In this paper we propose a new method of constructing canonical correlations and canonical variables for a pair of stochastic processes represented by a finite number of orthonormal basis functions.
LA - eng
KW - functional data; orthonormal basis; stochastic processes; canonical correlation analysis
UR - http://eudml.org/doc/268715
ER -
References
top- Krzyśko M. (2009): Podstawy wielowymiarowego wnioskowania statysty- cznego [Foundations of multidimensional statistical inference]. Wydawnictwo Naukowe UAM, Poznan.
- Leurgans S.E., Moyeed R.A., Silverman B.W. (1993): Canonical correlation analy- sis when the data are curves. Journal of the Royal Statistical Society B 55(3): 725{740. Zbl0803.62049
- Ramsay J.O., Danzell C.J. (1991): Some tools for functional data analysis. Journal of the Royal Statistical Society B 53: 539-572. Zbl0800.62314
- Ramsay J.O., Silverman B.W. (2005): Functional Data Analysis. Second Edition, Springer. Zbl1079.62006
- Schott J.R. (2005): Matrix Analysis for Statistics. Second Edition, Wiley, New York. Zbl1076.15002
- Seber G.A.F. (1984): Multivariate Observations. Wiley, New York.
- Shmueli G. (2010): To explain or to predict? Statistical Science 25(3): 289{310. [Crossref][WoS] Zbl1329.62045
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