Quadratures over graphs via the Frank-Wolfe method and its variant

Abstract

The choice of the norm on a space of functions over a graph is important to obtain a good quadrature. In this study, we consider numerical integration on an undirected and unweighted graph. Existing studies have defined various kinds of norms, which define a kind of ``smoothness" of functions over a graph. In this study, we used the norm defined by [Seto, Suda and Taniguchi, Linear Algebra Appl. (2014)]. and kernel quadrature techniques, the Frank--Wolfe and away-steps Frank--Wolfe method. We obtain a theoretical guarantee of the convergence of the away-steps Frank--Wolfe method.