Multiscale Weisfeiler-Leman Directed Graph Neural Networks for Prerequisite-Link Prediction

Prerequisite-link Prediction (PLP) aims to discover the condition relations of a specific event or a concerned variable, which is a fundamental problem in a large number of fields, such as educational data mining. Current studies on PLP usually developed graph neural networks (GNNs) to learn the representations of pairs of nodes. However, these models fail to distinguish non-isomorphic graphs and integrate multiscale structures, leading to the insufficient expressive capability of GNNs. To this end, we in this paper proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-dimensional Weisferiler-Leman directed GNNs, dubbed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-WediGNNs, to recognize non-isomorphic graphs via the Weisferiler-Leman algorithm. Furthermore, we integrated the multiscale structures of a directed graph into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-WediGNNs, dubbed multiscale <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-WediGNNs, from the bidirected views of in-degree and out-degree. With the Siamese network, the proposed models are extended to address the problem of PLP. Besides, the expressive power is then interpreted via theoretical proofs. The experiments were conducted on four publicly available datasets for concept prerequisite relation prediction (CPRP). The results show that the proposed models achieve better performance than the state-of-the-art approaches, where our multiscale <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i>-WediGNN achieves a new benchmark in the task of CPRP.