Subgraph-Mamba: Subgraph Mamba model with positional encoding

Subgraph representation learning is a crucial area within graph representation learning. However, existing methods face challenges in capturing the dependencies among subgraph nodes and addressing the inaccuracies in node features caused by subgraph overlaps. To address these challenges, this paper proposes a method called Subgraph Mamba Model with Positional Encoding (Subgraph-Mamba). Specifically, first, Subgraph-Mamba employs Graph Convolution with Different Weights (GDW) to update node features across the entire graph and to extract node features for subgraphs. Second, Subgraph-Mamba introduces a novel positional encoding method called Sine Projection Positional Encoding (SPPE) to calculate the positional encoding of subgraphs. This positional encoding is then incorporated into the subgraph node features to obtain subgraph node features with positional encoding. Third, Subgraph-Mamba proposes a Multi-head Mamba module to capture the dependencies among subgraph node features with positional encoding. As far as we know, this is the first paper to apply Mamba to subgraph representation learning. Finally, Subgraph-Mamba aggregates the subgraph node features, and the dependencies form a superior subgraph feature representation. Extensive experiments on multiple datasets demonstrate that Subgraph-Mamba outperforms state-of-the-art baselines. The source code can be found on this link: https://github.com/denggaoqin/Subgraph-Mamba.