Multi-Scale Geo-Temporal Crime Embedding (MSG-TCE): A Hierarchical Spatiotemporal Framework for Crime Prediction with Hyperbolic Spatial Pooling and Periodic Transformers

Crime prediction in urban environments is a complex and pressing challenge driven by the intricate interplay of spatiotemporal dependencies, hierarchical geographic patterns, and socio-environmental determinants. We propose a multi-scale geo-temporal crime embedding (MSG-TCE) framework, which hierarchically models these dynamics via three novel components: a hierarchical residual temporal encoder (HRTE), a periodic transformer Encoder (PTE), and a hyperbolic spatial pooler (HSP). The HRTE captures multi-scale temporal trends by combining dilated convolutions with residual connections, while the PTE explicitly encodes periodic crime patterns using self-attention conditioned on cyclical positional encodings. The HSP maps spatial crime hotspots into hyperbolic space to better represent their inherent hierarchical structure, spanning city–district–neighbourhood–street-segment scales, and aggregates neighbourhood information via graph convolutions. These components are fused through a gated cross-attention mechanism, yielding a unified embedding for crime prediction. Experiments on real-world datasets from Chicago, Los Angeles, and New York City demonstrate that MSG-TCE achieves consistent improvements over five competitive baselines across RMSE, Precision@20, and DTW metrics, with statistically significant gains at longer prediction horizons. Ablation studies confirm the contribution of each component. Spatial visualisation maps, robustness analyses, and an exploratory covariate-augmented variant further substantiate the empirical validity of the framework. This paper also discusses limitations, including data reporting biases, the need for full covariate integration, and ethical considerations, pertaining to algorithmic fairness in crime prediction.