Spatial Fuzzy Clustering Using Varying Coefficients

Abstract

To consider spatial information in spatial clustering, the Neighborhood Expectation-Maximization (NEM) algorithm incorporates a spatial penalty term in the objective function. Such an addition leads to multiple iterations in the E-step. Besides, the clustering result depends mainly on the choice of the spatial coefficient, which is used to weigh the penalty term but is hard to determine a priori. Furthermore, it may not be appropriate to assign a fixed coefficient to every site, regardless of whether it is in the class interior or on the class border. In estimating class posterior probabilities, sites in the class interior should receive stronger influence from their neighbors than those on the border. To that end, this paper presents a variant of NEM using varying coefficients, which are determined by the correlation of explanatory attributes inside the neighborhood. Our experimental results on real data sets show that it only needs one iteration in the E-step and consequently converges faster than NEM. The final clustering quality is also better than NEM.