New Penalties Improve Graph Autoencoders for Dynamic Graph Embedding

Graph autoencoders (GAEs) are widely used to learn representations for dynamic graphs, but their standard optimization objectives often overlook the structural differences between nodes. This research proposes three new variants of distance-based GAEs that integrate structural penalties directly into their reconstruction loss function. These variants all employ a two-layer Graph Convolutional Network (GCN) encoder and a Euclidean-distance decoder. The key innovation lies in extending the sparsity-corrected loss with two node-level regularization terms: one based on degree centrality (a hub penalty) and another derived from Natural Community Local Intrinsic Dimensionality (NC-LID). The motivation stems from prior observations that high NC-LID values are associated with reduced embedding quality. The goal of these penalties is to emphasize reconstruction errors for nodes that are structurally ambiguous or challenging to embed. Experiments conducted on multiple dynamic graph datasets demonstrate that incorporating NC-LID-based regularization consistently outperforms both the baseline GAE without structural regularization and the method using only hub-aware regularization, highlighting NC-LID as a valuable signal for enhancing dynamic graph autoencoders.