Halting In Randomwalk Kernels

Random walk kernels measure graph similarity by counting matching walks in two graphs. In their most popular form of geometric random walk kernels, longer walks of length k are downweighted by a factor of lambda(k) (lambda < 1) to ensure convergence of the corresponding geometric series. We know from the fi eld of link prediction that this downweighting often leads to a phenomenon referred to as halting: Longer walks are downweighted so much that the similarity score is completely dominated by the comparison of walks of length 1. This is a naive kernel between edges and vertices. We theoretically show that halting may occur in geometric random walk kernels. We also empirically quantify its impact in simulated datasets and popular graph classi fi cation benchmark datasets. Our fi ndings promise to be instrumental in future graph kernel development and applications of random walk kernels.