  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.
