Title: Nonlinear and additive principal component analysis for functional data
Authors: Jun Song - Korea University (Korea, South) [presenting]
Abstract: A nonlinear and additive version of principal component analysis for vector-valued random functions defined on an interval is developed. This is a generalization of functional principal component analysis that allows the relations among the random functions involved to be nonlinear. The method is constructed via two additively nested Hilbert spaces of functions, in which the first space characterizes the functional nature of the data, and the second space captures the nonlinear dependence. In the meantime, additivity is imposed so that we can avoid high-dimensional kernels in the functional space, which causes the curse of dimensionality. Simulation results show that the new method performs better than functional principal component analysis when the relations among random functions are nonlinear. We apply the new method to online handwritten digits data sets.