Representing spatial dependence and heterogeneity via deep kriging and compressed sensing for urban human activity intensity forecasting

Forecasting the spatiotemporal distribution of urban human activity intensity is crucial for intelligent urban management but remains challenging due to complex temporal dynamics and geospatial effects. While advanced deep learning models have effectively addressed complex dynamics, they are not designed from a geospatial perspective and often struggle to capture spatial dependence and heterogeneity. Rather than redesigning forecasting models, a more efficient approach is to incorporate geospatial effects using scalable, model-agnostic representation embeddings. However, existing representation methods primarily consider basic geospatial characteristics (e.g. locations, attributes, and relationships), failing to capture more complex geospatial effects. Furthermore, these methods are typically contrastive rather than predictive, limiting their utility for spatiotemporal forecasting. To address these issues, we proposed a novel Kriging and Compressed sensing-based Representation Learning framework (KCRL). This framework (1) employs spatial interpolation and reconstruction to generate embeddings that are more suitable for spatiotemporal forecasting tasks, and (2) leverages kriging and compressed sensing theories to reshape the learning mechanism, enabling it to capture spatial dependence and heterogeneity. Experiments on four real-world datasets of urban human activity intensity demonstrated that, using our KCRL framework, even a simple fully connected neural network could achieve better accuracy than state-of-the-art forecasting models.