Local Optimisation of Nyström Samples Through Stochastic Gradient Descent

Abstract We study a relaxed version of the column-sampling problem for Nyström approximation kernel matrices, where approximations are defined from multisets landmark points in ambient space; such referred to as samples. consider an unweighted variation radial squared-kernel discrepancy (SKD) criterion surrogate classical criteria used assess accuracy; this setting, we discuss how samples can be efficiently optimised through stochastic gradient descent. perform numerical experiments which demonstrate that local minimisation SKD yields with improved accuracy terms trace, Frobenius and spectral norms.