Spatially and Robustly Hybrid Mixture Regression Model for Inference of Spatial Dependence
Spatially and Robustly Hybrid Mixture Regression Model for Inference of Spatial Dependence
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DOI：
10.1109/icdm51629.2021.00013
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Wennan Chang;Pengtao Dang;Changlin Wan;Xiaoyu Lu;Yue Fang;Tong Zhao;Y. Zang;Bo Li;Chi Zhang;Sha Cao
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文献类型：
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作者：
Wennan Chang;Pengtao Dang;Changlin Wan;Xiaoyu Lu;Yue Fang;Tong Zhao;Y. Zang;Bo Li;Chi Zhang;Sha Cao
在本文中，我们提出了一个空间稳健混合回归模型来研究空间域上响应变量和一组解释变量之间的关系，假设这些关系可能呈现出不能用恒定回归系数捕捉的复杂的空间动态模式。我们的方法将稳健的有限混合高斯回归模型与空间约束相结合，同时处理空间非平稳性、局部均匀性和离群点污染。与现有的空间回归模型相比，我们提出的模型假设存在一些不同的回归模型，这些回归模型是基于表现出相似响应-预测关系的观测来估计的。因此，所提出的模型不仅解释了空间趋势的非平稳性，而且还将观测聚集到几个不同的同质组中。这在解释上提供了一个优势，因为确定了几个固定子过程，这些子过程捕捉到了响应变量和预测变量之间的主要关系。此外，该方法结合了稳健的程序来处理来自回归异常值和空间异常值的污染。通过这样做，我们稳健地将空间域分割成具有相似回归系数的不同局部区域，以及纯粹是异常值的零星位置。已经设计了严格的统计假设检验程序来检验这种分割的重要性。与其他稳健的有限混合回归、空间回归和空间分割方法相比，在大量合成和真实数据集上的实验结果证明了该方法的稳健性、准确性和有效性。
In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial non-stationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for non-stationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods.