T2-GNN: Graph Neural Networks for Graphs with Incomplete Features and Structure via Teacher-Student Distillation

Graph Neural Networks (GNNs) have been a prevailing technique for tackling various analysis tasks on graph data. A key premise for the remarkable performance of GNNs relies on complete and trustworthy initial graph descriptions (i.e., node features and graph structure), which is often not satisfied since real-world graphs are often incomplete due to various unavoidable factors. In particular, GNNs face greater challenges when both node features and graph structure are incomplete at the same time. The existing methods either focus on feature completion or structure completion. They usually rely on the matching relationship between features and structure, or employ joint learning of node representation and feature (or structure) completion in the hope of achieving mutual benefit. However, recent studies confirm that the mutual interference between features and structure leads to the degradation of GNN performance. When both features and structure are incomplete, the mismatch between features and structure caused by the missing randomness exacerbates the interference between the two, which may trigger incorrect completions that negatively affect node representation. To this end, in this paper we propose a general GNN framework based on teacher-student distillation to improve the performance of GNNs on incomplete graphs, namely T2-GNN. To avoid the interference between features and structure, we separately design feature-level and structure-level teacher models to provide targeted guidance for student model (base GNNs, such as GCN) through distillation. Then we design two personalized methods to obtain well-trained feature and structure teachers. To ensure that the knowledge of the teacher model is comprehensively and effectively distilled to the student model, we further propose a dual distillation mode to enable the student to acquire as much expert knowledge as possible.Comment: Accepted by AAAI2

On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels

The q-composite key predistribution scheme [1] is used prevalently for secure communications in large-scale wireless sensor networks (WSNs). Prior work [2]-[4] explores topological properties of WSNs employing the q-composite scheme for q = 1 with unreliable communication links modeled as independent on/off channels. In this paper, we investigate topological properties related to the node degree in WSNs operating under the q-composite scheme and the on/off channel model. Our results apply to general q and are stronger than those reported for the node degree in prior work even for the case of q being 1. Specifically, we show that the number of nodes with certain degree asymptotically converges in distribution to a Poisson random variable, present the asymptotic probability distribution for the minimum degree of the network, and establish the asymptotically exact probability for the property that the minimum degree is at least an arbitrary value. Numerical experiments confirm the validity of our analytical findings.Comment: Best Student Paper Finalist in IEEE International Symposium on Information Theory (ISIT) 201