Minimum entropy principle guided graph neural networks

Graph Neural Networks (GNNs) have become the mainstream way of learning graphstructured data consisting of nodes and edges. Generally, GNNs encode nodes and graphs to lower-dimensional vectorized representations for serving node-level and graphlevel downstream tasks, respectively. However, the dimension estimation issue (i.e., estimating the optimal dimension for representations) has been ignored by existing GNNs. Inappropriate representation dimensions will lead to sub-optimal performance of GNNs. To estimate the optimal representation dimensions for both node-level and graph-level representations, we propose a minimum entropy principle-guided dimension estimation framework MEDE. By considering the graph attribute and structure together, we carefully define the graph entropy of a graph. The optimal representation dimension of a single graph and its nodes can be obtained by minimizing the graph entropy. In addition, for graph representation learning involving multi-graphs, MEDE empowers GNNs to embed graphs into a candidate set of optimal graph representation dimensions, and each graph will be assigned a best-fit representation dimension. Experiments on the node and graph classification tasks and the network embedding task verify the effectiveness of minimum entropy principle-guided representation dimension estimation.