Spatial interpolation is essential for handling sparsity and missing spatial data. Current machine learning-based spatial interpolation methods are subject to the statistical constraints of spatial stratified heterogeneity (SSH), normally involving separate modeling of each stratum and simple weighted averaging to integrate intra-stratum and inter-strata features. However, these models overlook the different contributions of inter-strata features to different locations within a stratum (heterogeneous inter-strata associations, HIA) and the explanation of spatial effects on the interpolation process, leading to suboptimal and unreliable interpolation outcomes. This article proposes a novel explainable spatial interpolation method considering SSH (X-SSHM). Spatial and environmental features are utilized to describe intra-stratum and inter-strata information, which are fed into random forest-based learners to achieve high-level semantic feature mapping. Geographically weighted regression is employed to integrate intra-stratum and inter-strata features to achieve a unified expression of SSH and HIA, obtaining the final interpolation result. Geographically weighted Shapley (GSHAP) is proposed to decompose the marginal contributions of intra-stratum and inter-strata features. Model performance is evaluated on simulated and soil organic matter datasets. X-SSHM outperformed five baselines regarding interpolation accuracy. Moreover, statistical methods validated X-SSHM’s ability to elucidate the mechanisms by which SSH, spatial autocorrelation and HIA affect the model interpolation process.

Accurate and reliable traffic flow data are essential for intelligent transportation systems; however, limitations arising from hardware and communication costs often lead to missing data. Tensor decomposition is widely used to address these issues. However, existing imputation methods employ a fixed geographic feature similarity matrix to constrain the tensor decomposition process, which fails to accurately capture the spatial heterogeneity of traffic flows, thus limiting the imputation accuracy and robustness. This study proposes a tensor decomposition method embedded with geographic meta-knowledge (Meta-TD) to accurately determine the spatial heterogeneity of traffic flows. The key innovation is establishing a dynamic relationship between the geographic meta-knowledge and spatial heterogeneity of traffic flows, and then using the spatial heterogeneity of the traffic flows to constrain the tensor decomposition process. Experimental results based on real urban traffic flows demonstrated the superiority of Meta-TD over fifteen baseline models under random, block, and long time-series missing patterns, achieving reductions in MAE, RMSE, and MAPE of 6.97–97.05%, 3.33–94.68%, and 0.72–90.89%, respectively. Notably, Meta-TD maintained high accuracy for sudden changes in traffic flow states, evidencing its robustness to varying missing data rates and distribution patterns. This adaptability makes it highly suitable for complex and dynamic urban traffic environments.

Automatic road extraction has gained significant attention in urban navigation, sustainable transport, and disaster response. Conventional convolutional neural networks (CNNs) operate within the local receptive field, limiting their capacity to represent potential global relations between roads and surroundings. In addition, the edge is important topological information for road targets. Several works focus on predicting precise boundaries to enhance road extraction. However, over fit edges and the course integration between features of different network layers may lead to loss of local details and incorrect road segmentation results. Therefore, the Road-detail Preserving Mapper (RoadDP-Mapper) framework is proposed. First, RoadDP-Mapper employs a hierarchical transformer as the encoder to enable local-to-global reasoning. The asymmetric upsampling layers (APLs) are introduced to enhance the model’s capability to perceive and reconstruct critical road detail information. Second, a road edge-constrained branch with a detail preservation module (DPM) is devised to amplify the distinction between roads and backgrounds by extracting and preserving explicit class boundary details. The proposed joint loss inspires the transformer to capture the contextual spatial relationships while preserving the fine-grained features of the road. We evaluated our framework on the DeepGlobe dataset and self-annotated images from ten representative cities in China. The proposed framework has demonstrated its effectiveness by significantly reducing both missed detections and false alarms in road extraction. Furthermore, spatial transfer experiments have confirmed the generalizability of RoadDP-Mapper for large-scale road mapping.

Ensemble learning synthesizes the advantages of different models and has been widely applied in the field of spatial prediction. However, the nonlinear constraints of spatial heterogeneity on the model ensemble process make it difficult to adaptively determine the ensemble weights, greatly limiting the predictive ability of the ensemble learning model. This paper therefore proposes a novel geographical spatial heterogeneous ensemble learning method (GSH-EL). Firstly, the geographically weighted regression model, geographically optimal similarity model, and random forest model are used as three base learners to express local spatial heterogeneity, global feature correlation, and nonlinear relationship of geographic elements, respectively. Then, a spatially weighted ensemble neural network module (SWENN) of GSH-EL is proposed to express spatial heterogeneity by exploring the complex nonlinear relationship between the spatial proximity and ensemble weights. Finally, the outputs of the three base learners are combined with the spatial heterogeneous ensemble weights from SWENN to obtain the spatial prediction results. The proposed method is validated on the PM2.5 air quality and landslide dataset in China, both of which obtain more accurate prediction results than the existing ensemble learning strategies. The results confirm the need to accurately express spatial heterogeneity in the model ensemble process.