A Comparative Study of Loss Functions for Short-Range Crime Forecasting: Enhancing Embedding Generation for Visualization Systems

• Aline Martins Nascimento Belchior USP
• Raissa Rosa dos Santos Januario USP
• Marvin Mendes Cabral USP
• Luis Gustavo Nonato USP

DOI: https://doi.org/10.5753/sibgrapi.est.2025.38299

Resumo

Criminal incidents have complex socio-economic impacts and reduce the population’s perceived security. Accurate short-term crime-rate forecasting enables more efficient allocation of policing resources and better strategic decisions to mitigate criminal activity. Transformer-based architectures are effective at capturing complex temporal dependencies in time series forecasting; however, model behaviour and the structure of learned representations are strongly influenced by the training loss. In this work, we present a comparative analysis of Transformer and recurrent architectures trained with two different losses, the Mean Squared Error (MSE) and the Soft Dynamic Time Warping (Soft-DTW), with focus on short-term forecasting of vehicle thefts in São Paulo. Our goal is to produce embeddings that are more representative of crime dynamics and thus more useful for downstream tasks such as visualization and pattern analysis. We evaluate Autoformer, ITransformer, and Informer alongside LSTM and GRU baselines, using three performance metrics: MSE, MAE and DTW. Overall, models trained with the DTW-based loss achieved performance similar to, or slightly worse than, those trained with MSE; an important exception is the Autoformer, which showed improved accuracy with Soft-DTW at the 14-day horizon. We discuss several factors that likely affected these results: (i) the short forecasting horizons studied, (ii) the formulation of the prediction task (forecasting the entire aggregated series may not be optimal), and (iii) aggregation to daily city-level counts, which discards spatial heterogeneity and may remove salient signal. These findings motivate further experiments (e.g., multi-scale and spatially resolved forecasting) to more comprehensively assess the comparative effectiveness of Soft-DTW and MSE for criminal time series prediction.

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