Kernel functional canonical correlation analysis
DOI:
https://doi.org/10.18778/0208-6018.325.12Keywords:
Functiona data, Canonical correlation analysis, KernelAbstract
Canonical correlation methods for data representing functions or curves have received much attention in recent years. Such data, known in the literature as functional data (Ramsay and Silverman, 2005), has been the subject of much recent research interest. Examples of functional data can be found in several application domains, such as medicine, economics, meteorology and many others. Unfortunately, the multivariate data canonical correlation methods cannot be used directly for functional data, because of the problem of dimensionality and difficulty in taking into account the correlation and order of functional data. The problem of constructing canonical correlations and canonical variables for functional data was addressed by Leurgans et al. (1993), and further developments were made by Ramsay and Silverman (2005). In this paper we propose a new method of constructing canonical correlations and canonical variables for functional data.
Downloads
References
Aronszajn N. (1950), Theory of reproducing kernels, “Trans. Amer. Math. Soc.” 68, p. 337–404.
Google Scholar
Friedman J. H. (1989), Regularized Discriminant Analysis., “J. Amer. Statist. Assoc.” 84, p. 165.
Google Scholar
Krzyśko M., Waszak Ł. (2013), Canonical correlation analysis for functional data, “Biometrical Letters”.
Google Scholar
Leurgans S.E., Moyeed R.A., Silverman B.W. (1993), Canonical correlation analysis when the data are curves, “Journal of the Royal Statistical Society”, Series B 55, p. 725–740.
Google Scholar
Ramsay J.O., Silverman B.W. (2005), Functional Data Analysis, Second Edition. Springer.
Google Scholar
Shmueli G. (2010), To explain or to predict?, “Statistical Science” 25(3), p. 289–310.
Google Scholar
The online database of the World Bank: http://data.worldbank.org/
Google Scholar