  Factorization machine (FM) is a prevalent approach to modeling pairwise
(second-order) feature interactions when dealing with high-dimensional sparse
data. However, on the one hand, FM fails to capture higher-order feature
interactions suffering from combinatorial expansion. On the other hand, taking
into account interactions between every pair of features may introduce noise
and degrade prediction accuracy. To solve the problems, we propose a novel
approach, Graph Factorization Machine (GraphFM), by naturally representing
features in the graph structure. In particular, we design a mechanism to select
the beneficial feature interactions and formulate them as edges between
features. Then the proposed model, which integrates the interaction function of
FM into the feature aggregation strategy of Graph Neural Network (GNN), can
model arbitrary-order feature interactions on the graph-structured features by
stacking layers. Experimental results on several real-world datasets have
demonstrated the rationality and effectiveness of our proposed approach. The
code and data are available at
\href{https://github.com/CRIPAC-DIG/GraphCTR}{https://github.com/CRIPAC-DIG/GraphCTR}.
