Gaussian RBF Centered Kernel Alignment (CKA) in the Large Bandwidth Limit

Abstract--We prove that Centered Kernel Alignment (CKA) based on a Gaussian RBF kernel converges to linear CKA in the large-bandwidth limit. We show that convergence onset is sensitive to the geometry of the feature representations, and that representation eccentricity bounds the range of bandwidths for which Gaussian CKA behaves nonlinearly. Centered Kernel Alignment (CKA) was first proposed as a large-bandwidth asymptotics of Gaussian CKA. A limit result measure of similarity between kernels in the context of kernel for Gaussian kernel SVM classification appeared in [17], but learning [1], [2], building on prior work on (non-centered) relies on an analysis of the dual formulation of the maximummargin kernel-target alignment [3]. Versions for functional data optimization problem that does not translate directly of CKA and the associated Hilbert-Schmidt Independence to kernel CKA.