Structural and positional ensembled encoding for Graph Transformer

In the Transformer architecture, positional encoding is a vital component because it provides the model with information about the structure and position of data. In Graph Transformer, there have been attempts to introduce different positional encodings and inject additional structural information. Therefore, in terms of integrating positional and structural information, we propose a Structural and Positional Ensembled Graph Transformer (SPEGT). We developed SPEGT by noting the different properties of structural and positional encodings of graphs and the similarity of their computational processes. We have set a unified component that integrates the functionalities: (i) Random Walk Positional Encoding, (ii) Shortest Path Distance between each node, and (iii) Hierarchical Cluster Encoding. We find a problem with a well-known positional encoding and experimentally verify that combining it with other encodings can solve their problem. In addition, SPEGT outperforms previous models on a variety of graph datasets. We also show that SPEGT using unified positional encoding, performs well on structurally indistinguishable graph data through error case analysis.