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| | Hui-Lang Xu1,2,3,et al.[en_title][J].Control Theory and Technology,2024,22(1):135~146.[Copy] |
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| Variable projection algorithms with sparse constraint for separable nonlinear models |
| Hui-LangXu1,2,3,4,Guang-YongChen1,2,3,4,Si-QingCheng1,MinGan1,JingChen5 |
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| (1 College of Computer and Data Science, Fuzhou University, Fuzhou 350116, Fujian, China;
2 Fujian Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou 350116, Fujian, China;
3 Key Laboratory of Intelligent Metro of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, China;
4 Engineering Research Center of Big Data Intelligence, Ministry of Education, Fuzhou University, Fuzhou 350116, Fujian, China;;5 School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China.) |
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| 摘要: |
| Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine
learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of
these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous
theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable
nonlinear models, but these are based on L2 penalty of model parameters, which cannot be directly extended to deal with
sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradientbased and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear
parameters under sparse constraint; and how to deal with the coupling relationship between linear and nonlinear parameters in
the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness
of the proposed algorithms. |
| 关键词: Variable projection (VP) · Non-smooth constraint · Separable nonlinear models |
| DOI：https://doi.org/10.1007/s11768-023-00194-3 |
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| 基金项目:This work was supported in part by the National Nature Science Foundation of China (Nos. 62173091, 62073082), in part by the Natural Science Foundation of Fujian Province (No. 2023J01268) and in part by the Taishan Scholar Program of Shandong Province. |
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| Variable projection algorithms with sparse constraint for separable nonlinear models |
| Hui-Lang Xu1,2,3,4,Guang-Yong Chen1,2,3,4,Si-Qing Cheng1,Min Gan1,Jing Chen5 |
| (1 College of Computer and Data Science, Fuzhou University, Fuzhou 350116, Fujian, China;
2 Fujian Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou 350116, Fujian, China;
3 Key Laboratory of Intelligent Metro of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, China;
4 Engineering Research Center of Big Data Intelligence, Ministry of Education, Fuzhou University, Fuzhou 350116, Fujian, China;;5 School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China.) |
| Abstract: |
| Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine
learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of
these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous
theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable
nonlinear models, but these are based on L2 penalty of model parameters, which cannot be directly extended to deal with
sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradientbased and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear
parameters under sparse constraint; and how to deal with the coupling relationship between linear and nonlinear parameters in
the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness
of the proposed algorithms. |
| Key words: Variable projection (VP) · Non-smooth constraint · Separable nonlinear models |
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