Discovering Spatial Mixture Patterns of Interest

Given a collection of N geo-located point samples of k types, we aim to detect spatial mixture patterns of interest, which are sub-regions of the study area that have significantly high or low mixture of points of different types. Spatial mixture patterns have important applications in many societal domains, including resilience of smart cities and communities, biodiversity, equity, business intelligence, etc. The problem is challenging because ranking and selection of candidate patterns can be highly susceptible to the effect of natural randomness, and real-world data often consists of various mixture patterns. In related work, the multi-nomial scan statistic does not support identification of high or low mixture due to its "directionless" nature and high sensitivity to the composition of mixture patterns in data. While species richness indices in biodiversity research allow specification of directions, the measures are very sensitive to spatial randomness effects. To bridge the gap, we first propose a spatial mixture index to provide robust ranking among candidate patterns. Then, we present a dual-level Monte-Carlo estimation method with a baseline algorithm for spatial mixture pattern detection. Finally, we propose both an exact algorithm and a distribution-inspired sequence-reduction heuristic to accelerate the baseline approach. Experiment results with both synthetic and real-world data show that the proposed approaches can detect mixture patterns with high accuracy, and the acceleration methods can greatly reduce computational cost while maintaining high solution quality.