Causal invariant geographic network representations with feature and structural distribution shifts

Relationships between geographic entities, including human-land and human-people relationships, can be naturally modelled by graph structures, and geographic network representation is an important theoretical issue. The existing methods learn geographic network representations through deep graph neural networks (GNNs) based on the i.i.d. assumption. However, the spatial heterogeneity and temporal dynamics of geographic data make the out-of-distribution (OOD) generalisation problem particularly salient. We classify geographic network representations into invariant representations that always stabilise the predicted labels under distribution shifts and background representations that vary with different distributions. The latter are particularly sensitive to distribution shifts (feature and structural shifts) between testing and training data and are the main causes of the out-of-distribution generalisation (OOD) problem. Spurious correlations are present between invariant and background representations due to selection biases/environmental effects, resulting in the model extremes being more likely to learn background representations. The existing approaches focus on background representation changes that are determined by shifts in the feature distributions of nodes in the training and test data while ignoring changes in the proportional distributions of heterogeneous and homogeneous neighbour nodes, which we refer to as structural distribution shifts. We propose a feature-structure mixed invariant representation learning (FSM-IRL) model that accounts for both feature distribution shifts and structural distribution shifts. To address structural distribution shifts, we introduce a sampling method based on causal attention, encouraging the model to identify nodes possessing strong causal relationships with labels or nodes that are more similar to the target node. This approach significantly enhances the invariance of the representations between the source and target domains while reducing the dependence on background representations that arise by chance or in specific patterns. Inspired by the Hilbert-Schmidt independence criterion, we implement a reweighting strategy to maximise the orthogonality of the node representations, thereby mitigating the spurious correlations among the node representations and suppressing the learning of background representations. In addition, we construct an educational-level geographic network dataset under out-of-distribution (OOD) conditions. Our experiments demonstrate that FSM-IRL exhibits strong learning capabilities on both geographic and social network datasets in OOD scenarios.