An entropy-based method for assessing the number of spatial outliers

A spatial outlier is a spatial object whose non-spatial attributes are significantly different from those of its spatial neighbors. A major limitation associated with the existing outlier detection algorithms is that they generally require a pre-specified number of spatial outliers. Estimating an appropriate number of outliers for a spatial data set is one of the critical issues for outlier analysis. This paper proposes an entropy-based method to address this problem. We define the function of spatial local contrast entropy. Based on the local contrast and local contrast probability that derived from non-spatial and spatial attributes, the spatial local contrast entropy can be computed. By incrementally removing outliers, the entropy value will keep decreasing until it becomes stable at a certain point, where an optimal number of outliers can be estimated. We considered both the single attribute and the multiple attributes of spatial objects. Experiments conducted on the US Housing data validated the effectiveness of our proposed approach.