Hypergraph pp-Laplacian: A Differential Geometry View

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph $p$-Laplacian. Unlike the existing two-node graph Laplacians, this generalization makes it possible to analyze hypergraphs, where the edges are allowed to connect any number of nodes. Moreover, we propose a semi-supervised learning method based on the proposed hypergraph $p$-Laplacian, and formalize them as the analogue to the Dirichlet problem, which often appears in physics. We further explore theoretical connections to normalized hypergraph cut on a hypergraph, and propose normalized cut corresponding to hypergraph $p$-Laplacian. The proposed $p$-Laplacian is shown to outperform standard hypergraph Laplacians in the experiment on a hypergraph semi-supervised learning and normalized cut setting.Comment: Extended version of our AAAI-18 pape

Multi-level Graph Convolutional Networks for Cross-platform Anchor Link Prediction

© 2020 ACM. Cross-platform account matching plays a significant role in social network analytics, and is beneficial for a wide range of applications. However, existing methods either heavily rely on high-quality user generated content (including user profiles) or suffer from data insufficiency problem if only focusing on network topology, which brings researchers into an insoluble dilemma of model selection. In this paper, to address this problem, we propose a novel framework that considers multi-level graph convolutions on both local network structure and hypergraph structure in a unified manner. The proposed method overcomes data insufficiency problem of existing work and does not necessarily rely on user demographic information. Moreover, to adapt the proposed method to be capable of handling large-scale social networks, we propose a two-phase space reconciliation mechanism to align the embedding spaces in both network partitioning based parallel training and account matching across different social networks. Extensive experiments have been conducted on two large-scale real-life social networks. The experimental results demonstrate that the proposed method outperforms the state-of-the-art models with a big margin