  Graph representation learning has achieved great success in many areas,
including e-commerce, chemistry, biology, etc. However, the fundamental problem
of choosing the appropriate dimension of node embedding for a given graph still
remains unsolved. The commonly used strategies for Node Embedding Dimension
Selection (NEDS) based on grid search or empirical knowledge suffer from heavy
computation and poor model performance. In this paper, we revisit NEDS from the
perspective of minimum entropy principle. Subsequently, we propose a novel
Minimum Graph Entropy (MinGE) algorithm for NEDS with graph data. To be
specific, MinGE considers both feature entropy and structure entropy on graphs,
which are carefully designed according to the characteristics of the rich
information in them. The feature entropy, which assumes the embeddings of
adjacent nodes to be more similar, connects node features and link topology on
graphs. The structure entropy takes the normalized degree as basic unit to
further measure the higher-order structure of graphs. Based on them, we design
MinGE to directly calculate the ideal node embedding dimension for any graph.
Finally, comprehensive experiments with popular Graph Neural Networks (GNNs) on
benchmark datasets demonstrate the effectiveness and generalizability of our
proposed MinGE.
