Canonical correlation analysis for functional data

• Autorzy: Mirosław Krzyśko , Łukasz Waszak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

functional data; orthonormal basis; stochastic processes; canonical correlation analysis

• Wydawca: De Gruyter Open
• Czasopismo: Biometrical Letters
• Rocznik: 2013
• Tom: 50
• Numer: 2
• Strony: 95-105

Daty

wydano

2013-12-01

online

2013-12-10

Twórcy

autor

Mirosław Krzyśko

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

Łukasz Waszak

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Bibliografia

• 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.
• Ramsay J.O., Danzell C.J. (1991): Some tools for functional data analysis. Journal of the Royal Statistical Society B 53: 539-572.
• Ramsay J.O., Silverman B.W. (2005): Functional Data Analysis. Second Edition, Springer.
• Schott J.R. (2005): Matrix Analysis for Statistics. Second Edition, Wiley, New York.
• 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]

Identyfikatory

DOI

10.2478/bile-2013-0020