Biometrical Letters Vol. 57(1), 2020, pp. 1-12
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GENERALIZED CANONICAL CORRELATION ANALYSIS FOR FUNCTIONAL DATA Tomasz Górecki1, Mirosław Krzysko2, Waldemar Wołynski1 1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznanskiego 4, 61-614 Poznan, Poland, e-mail: tomasz.gorecki@amu.edu.pl, wolynski@amu.edu.pl 2Interfaculty Institute of Mathematics and Statistics, The President Stanisław Wojciechowski State University of Applied Sciences in Kalisz, Nowy Swiat 4, 62-800 Kalisz, Poland, e-mail: mkrzysko@amu.edu.pl |
There is a growing need to analyze data sets characterized by several sets of variables observed on the same set of individuals. Such complex data structures are known as multiblock (or multiple-set) data sets. Multiblock data sets are encountered in diverse fields including bioinformatics, chemometrics, food analysis, etc. Generalized Canonical Correlation Analysis (GCCA) is a very powerful method to study this kind of relationships between blocks. It can also be viewed as a method for the integration of information from K > 2 distinct sources (Takane and Oshima-Takane 2002). In this paper, GCCA is considered in the context of multivariate functional data. Such data are treated as realizations of multivariate random processes. GCCA is a technique that allows the joint analysis of several sets of data through dimensionality reduction. The central problem of GCCA is to construct a series of components aiming to maximize the association among the multiple variable sets. This method will be presented for multivariate functional data. Finally, a practical example will be discussed.
multivariate functional data, generalized canonical correlation analysis
