Discovery of regularized areas with maximal confidence from location data

Abstract

We propose a new approach to discovering regions optimizing the expected responses from data with a strong spatial bias. The methods available thus far do not work well on data of that nature because they assume that coordinates and responses are uniform and isotropic. To relax this assumption, we employ a hypothesis that cells in an irregularly sized mesh are connected transitively. However, it requires considerable computation and possibly overfits data because there are exponentially many transitive closures. Our contributions to overcome these problems are twofold: we prove the maximal property that shows how irrelevant cells are removed without enumerating candidates in the hypothesis space, and we propose a description length of transitive closure based on which the remaining regions are regularized. We show via experiments that our algorithms do not decrease the precision with unknown data, even when such data are neither uniform nor isotropic. In addition, we show that the regularized region improves the precision by more than 20% compared to the unregularized one.