函数型正则广义典型相关分析

An effective dimension reduction method for multivariate functional data is developed within the theoretical framework of regularized generalized canonical correlation analysis. Functional data in square integrable spaces is first projected in an integral form to a series of numeric variables, and those variables are then used for simultaneously determining the related projection directions of functional features by maximizing a kind of global correlation measure, which achieves the featured information extraction and rapid dimension reduction of multivariate functional data as traditional numeric variables. A general basis function system is used to create the iterative computing algorithm for the optimal functional projection weights, which is independent of the specified basis functions. A large number of simulation results for infinite samples show that the proposed method is able to detect the correlation among multivariate functional data and obtain consistent estimates for the associated functional projection weights. The real-data study on the gait of Parkinson’s patients indicates the interpretability of the numeric featured information derived from the original functional data and the utility of the proposed method.