A graph autoencoder network to measure the geometric similarity of drainage networks in scaling transformation

Similarity measurement has been a prevailing research topic in geographic information science. Geometric similarity measurement in scaling transformation (GSM_ST) is critical to ensure spatial data quality while balancing detailed information with distinctive features. However, GSM_ST is an uncertain problem due to subjective spatial cognition, global and local concerns, and geometric complexity. Traditional rule-based methods considering multiple consistent conditions require subjective adjustments to characteristics and weights, leading to poor robustness in addressing GSM_ST. This study proposes an unsupervised representation learning framework for automated GSM_ST, using a Graph Autoencoder Network (GAE) and drainage networks as an example. The framework involves constructing a drainage graph, designing the GAE architecture for GSM_ST, and using Cosine similarity to measure similarity based on the GAE-derived drainage embeddings in different scales. We perform extensive experiments and compare methods across 71 drainage networks during five scaling transformations. The results show that the proposed GAE method outperforms other methods with a satisfaction ratio of around 88% and has strong robustness. Moreover, our proposed method also can be applied to other scenarios, such as measuring similarity between geographical entities at different times and data from different datasets.