Kernel functional canonical correlation analysis

Abstract

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.