From Closing Triangles to Higher-Order Motif Closures for Better Unsupervised Online Link Prediction

This paper introduces higher-order link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as online visitor stitching, web search, and online recommendation. In such applications, real-time performance is critical. The proposed methods do not require any explicit training data, nor do they derive an embedding from the graph data, or perform any explicit learning. Most existing unsupervised methods with the above desired properties are all based on closing triangles (common neighbors, Jaccard similarity, and the ilk). In this work, we develop unsupervised techniques based on the notion of closing higher-order motifs that generalize beyond closing simple triangles. Through extensive experiments, we find that these higher-order motif closures often outperform triangle-based methods, which are commonly used in practice. This result implies that one should consider other motif closures beyond simple triangles. We also find that the "best" motif closure depends highly on the underlying network and its structural properties. Furthermore, all methods described in this work are fast for link prediction-based applications requiring real-time performance. The experimental results indicate the importance of closing higher-order motifs for unsupervised link prediction. Finally, these new higher-order motif closures can serve as a basis for studying and developing better unsupervised real-time link prediction and ranking methods.