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<p>With the development of sensor networks, the spatial–temporal relationships of multivariate time series also bring the challenge for multi-task spatial–temporal time series prediction in environmental datasets. In this paper, we propose the task-oriented and attractor regularized multi-task learning model (TOAR-MTL). In the model, random feature and Nyström approximation are adopted for hierarchical dynamics. Joint sparsity constraints are utilized for task-oriented feature selection, which could explore the dynamic-shared and dynamic-specific features. Simultaneously, the manifold regularization is adopted for attractor priori to constrain the predicted value back onto the attractor manifold. Furthermore, an efficient iterative algorithm based on the alternative direction multiplier method and accelerated proximal gradient method is proposed and a decoupling variable is introduced to handle the complex objective function. Simulations are conducted on the London, Beijing–Tianjin–Hebei, Lorenz and Beijing Air Quality datasets. The experiment results illustrate that the Nyström approximation could speed up the training process by 30–100 times and the task-oriented feature selection could adaptively obtain sparse interpretable weights. Therefore, the TOAR-MTL could effectively promote the multi-step prediction accuracy of environmental spatial–temporal time series.</p>

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Task-oriented and attractor regularized multi-task learning for environmental spatial–temporal time series prediction

  • 期刊论文

  • 发表日期：

    2025年6月21日

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  • Fei Lv,
  • Shuaizong Si,
  • Weijie Ren

摘要

With the development of sensor networks, the spatial–temporal relationships of multivariate time series also bring the challenge for multi-task spatial–temporal time series prediction in environmental datasets. In this paper, we propose the task-oriented and attractor regularized multi-task learning model (TOAR-MTL). In the model, random feature and Nyström approximation are adopted for hierarchical dynamics. Joint sparsity constraints are utilized for task-oriented feature selection, which could explore the dynamic-shared and dynamic-specific features. Simultaneously, the manifold regularization is adopted for attractor priori to constrain the predicted value back onto the attractor manifold. Furthermore, an efficient iterative algorithm based on the alternative direction multiplier method and accelerated proximal gradient method is proposed and a decoupling variable is introduced to handle the complex objective function. Simulations are conducted on the London, Beijing–Tianjin–Hebei, Lorenz and Beijing Air Quality datasets. The experiment results illustrate that the Nyström approximation could speed up the training process by 30–100 times and the task-oriented feature selection could adaptively obtain sparse interpretable weights. Therefore, the TOAR-MTL could effectively promote the multi-step prediction accuracy of environmental spatial–temporal time series.