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 nonstationarity, 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 nonstationarity 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.

翻译：在本文中,我们提出一个空间强力混凝土回归模型,以调查反应变量和一组空间域的解释变量之间的关系,假设这些关系可能呈现复杂的空间动态模式,而这种模式无法通过恒定回归系数所捕捉到。我们的方法将强势混合高斯回归模型与空间限制相结合,同时处理空间非常态、当地同质性和外部污染。与现有的空间回归模型相比,我们提议的模型假设存在一个少数不同的空间回归模型,这些模型根据显示类似反应-先质关系的观测结果估算。因此,拟议的模型不仅说明空间趋势中的不常态性,而且还将观测归为几个不同和同质的组别。我们的方法将强势混合的混合物回归模型纳入其中,同时处理空间非常态性、当地均匀性和外部污染;与现有的空间回归模型相比,我们将空间域分割成不同的地方区域,具有相似的倒退系数,因此,拟议模型不仅反映空间静态性,而且将观测结果分组零星系,从而完全超越了僵硬度。