Summary statistics of the experimental dataset.

With the rapid advancement of cross-border e-commerce, accurately predicting user purchase behavior has emerged as a critical challenge for enhancing platform operational efficiency and user experience. This study proposes a hybrid deep learning framework for predicting user purchase behavior in cross-border e-commerce. The model integrates Long Short-Term Memory (LSTM) networks with Variational Mode Decomposition (VMD) to forecast future user actions. The proposed methodology begins by applying VMD to preprocess raw behavioral time-series data, decomposing it into multiple intrinsic mode functions (IMFs) to mitigate noise and extract multi-frequency features, thereby enhancing data quality. The refined components are subsequently fed into an LSTM network to model long-term temporal dependencies and generate precise purchase predictions. Furthermore, Particle Swarm Optimization (PSO) is employed to automate the hyperparameter tuning of the LSTM model, effectively mitigating overfitting and improving generalization. Experimental evaluations demonstrate that the VMD-PSO-LSTM hybrid model achieves superior prediction accuracy and robustness compared to conventional approaches. The results underscore the efficacy of integrating signal decomposition, deep learning, and evolutionary optimization as a viable solution for behavioral prediction in cross-border e-commerce contexts.