Graph Filtration Kernels

The majority of popular graph kernels is based on the concept Haussler's R-convolution kernel and defines similarities in terms mutual substructures. In this work, we enrich these similarity measures by considering filtrations: Using meaningful orders set edges, which allow to construct a sequence nested graphs, can consider at multiple granularities. A key our approach track features over course such resolutions. Rather than simply compare frequencies allows for their comparison when how long they exist sequences. propose family that incorporate existence intervals features. While be applied arbitrary features, particularly highlight Weisfeiler-Lehman vertex labels, leading efficient kernels. We show using labels certain filtrations strictly increases expressive power ordinary procedure deciding isomorphism. fact, result directly yields more powerful has implications neural networks due close relationship method. empirically validate significant improvements state-of-the-art predictive performance various real-world benchmark datasets.