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YangNet: a nonlinear and nonstationary spatial interpolation method based on spatial compound variable theory.

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Title: YangNet: a nonlinear and nonstationary spatial interpolation method based on spatial compound variable theory.
Authors: Yang, Jie1 (AUTHOR), Liu, Qiliang1 (AUTHOR) qiliang.liu@csu.edu.cn, Mao, Xiancheng1 (AUTHOR), Liu, Zhankun1 (AUTHOR), Deng, Min1 (AUTHOR)
Source: International Journal of Geographical Information Science. Jan2026, Vol. 40 Issue 1, p112-139. 28p.
Subjects: Nonlinear statistical models, Graph neural networks, Stochastic processes, Spatial analysis (Statistics), Geographic spatial analysis, Geomatics
Geographic Terms: China
Abstract: Modeling nonstationary and nonlinear variations in spatial processes is challenging. To overcome this long-standing challenge in spatial interpolation, we introduced the spatial compound variable theory, which assumes that a spatial variable can be divided into global regular and local irregular components. We argue that nonstationary and nonlinear variations in these two components have distinct properties: the global regular component describes a nonlinear trend that is locally predictable, whereas the local irregular component represents local hotspots, cold spots, or outliers. Following the spatial compound variable theory, we developed a novel nonlinear and nonstationary spatial interpolation model by integrating Yang Chizhong filtering and an inductive graph convolution network (YangNet). Specifically, we used the Yang Chizhong filtering and interpolation method to estimate the global regular component with a nonlinear trend, built an inductive graph convolution network to model the nonlinear relationship between the estimated global regular component and the corresponding observation data, and used the nonlinear relationship to estimate the local irregular component. A case study of the Xiadian gold deposit in China demonstrates that YangNet outperforms four representative gold grade interpolation methods in terms of accuracy and smoothing effect mitigation. YangNet exhibits excellent adaptability and can be applied widely in geoscience. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Geographical Information Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: YangNet: a nonlinear and nonstationary spatial interpolation method based on spatial compound variable theory.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Geographical+Information+Science%22">International Journal of Geographical Information Science</searchLink>. Jan2026, Vol. 40 Issue 1, p112-139. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+statistical+models%22">Nonlinear statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+neural+networks%22">Graph neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Spatial+analysis+%28Statistics%29%22">Spatial analysis (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Geographic+spatial+analysis%22">Geographic spatial analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Geomatics%22">Geomatics</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22China%22">China</searchLink>
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  Data: Modeling nonstationary and nonlinear variations in spatial processes is challenging. To overcome this long-standing challenge in spatial interpolation, we introduced the spatial compound variable theory, which assumes that a spatial variable can be divided into global regular and local irregular components. We argue that nonstationary and nonlinear variations in these two components have distinct properties: the global regular component describes a nonlinear trend that is locally predictable, whereas the local irregular component represents local hotspots, cold spots, or outliers. Following the spatial compound variable theory, we developed a novel nonlinear and nonstationary spatial interpolation model by integrating Yang Chizhong filtering and an inductive graph convolution network (YangNet). Specifically, we used the Yang Chizhong filtering and interpolation method to estimate the global regular component with a nonlinear trend, built an inductive graph convolution network to model the nonlinear relationship between the estimated global regular component and the corresponding observation data, and used the nonlinear relationship to estimate the local irregular component. A case study of the Xiadian gold deposit in China demonstrates that YangNet outperforms four representative gold grade interpolation methods in terms of accuracy and smoothing effect mitigation. YangNet exhibits excellent adaptability and can be applied widely in geoscience. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Geographical Information Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1080/13658816.2025.2508840
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      – Code: eng
        Text: English
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        PageCount: 28
        StartPage: 112
    Subjects:
      – SubjectFull: Nonlinear statistical models
        Type: general
      – SubjectFull: Graph neural networks
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Spatial analysis (Statistics)
        Type: general
      – SubjectFull: Geographic spatial analysis
        Type: general
      – SubjectFull: Geomatics
        Type: general
      – SubjectFull: China
        Type: general
    Titles:
      – TitleFull: YangNet: a nonlinear and nonstationary spatial interpolation method based on spatial compound variable theory.
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      – PersonEntity:
          Name:
            NameFull: Yang, Jie
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            NameFull: Liu, Qiliang
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            NameFull: Mao, Xiancheng
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            NameFull: Liu, Zhankun
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            NameFull: Deng, Min
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            – D: 01
              M: 01
              Text: Jan2026
              Type: published
              Y: 2026
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