Speaker: Yuka Hashimoto, NTT Corporation

Date: September 22, 2022

Abstract: RKHM (Reproducing kernel Hilbert C*-module) is a generalization of RKHS (Reproducing kernel Hilbert space) and characterized by a C*-algebra-valued positive definite kernel and inner product induced by this kernel. Regarding RKHS, it has been actively researched for data analysis. RKHSs effectively handle nonlinearities in original data spaces. However, if the data space is a function space, RKHSs are not sufficient for capturing and extracting continuous behaviors of the data. Therefore, we consider using RKHMs instead of RKHSs for functional data. Since inner products in RKHMs are C*-algebra-valued, they capture more information about functions than complex-valued ones. We show some important properties available in RKHSs are also available in RKHMs.