With the acceleration of urbanization, the spatiotemporal characteristics of criminal activities have become increasingly complex. Accurate prediction of crime distribution is crucial for optimizing the allocation of police resources and preventing crime. This paper proposes LGSTime, a crime spatiotemporal prediction model that integrates Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and the Multi-head Sparse Self-attention mechanism. LSTM and GRU capture long-term dependencies in crime time series, such as seasonality and periodicity, through their unique gating mechanisms. The Multi-head Sparse Self-attention mechanism, on the other hand, focuses on both temporal and spatial features of criminal events simultaneously through parallel processing and sparsification techniques, significantly improving computational efficiency and prediction accuracy. The integrated model leverages the strengths of each technique to better handle complex spatiotemporal data. Experimental findings demonstrate that the model attains optimal performance across four real - world crime datasets. In comparison to the CNN model, it exhibits performance enhancements of 2.8\%, 1.9\%, and 1.4\% in the Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) metrics respectively. These results offer a valuable reference for tackling the challenges in crime prediction.

翻译：随着城市化进程的加速，犯罪活动的时空特征日趋复杂。准确预测犯罪分布对于优化警力资源配置和预防犯罪至关重要。本文提出LSGTime，一种融合长短期记忆网络（LSTM）、门控循环单元（GRU）与多头稀疏自注意力机制的犯罪时空预测模型。LSTM与GRU通过其独特的门控机制，能够捕捉犯罪时间序列中的长期依赖关系，如季节性与周期性特征。而多头稀疏自注意力机制则通过并行处理与稀疏化技术，同时关注犯罪事件的时序与空间特征，显著提升了计算效率与预测精度。该融合模型综合了各项技术的优势，以更好地处理复杂的时空数据。实验结果表明，该模型在四个真实犯罪数据集上均取得了最优性能。与CNN模型相比，其在均方误差（MSE）、平均绝对误差（MAE）与均方根误差（RMSE）指标上分别实现了2.8%、1.9%与1.4%的性能提升。这些结果为应对犯罪预测中的挑战提供了有价值的参考。