Discovering Spatial Mixture Patterns of Interest

Abstract

Given a collection of geo-located point samples of 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 realworld 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. CCS CONCEPTS • Information systems → Data mining; Spatial-temporal systems.

Mapping Mangrove Opportunities with Open Access Data: A Case Study for Bangladesh

“…Low diversity has been associated to large-scale death events due to pests in single species stands of mangroves [66][67][68], but this aspect has received relatively less attention in planting schemes. Spatial statistical techniques can offer powerful tools to evaluate risks associated with low biodiversity [69] and to create more resilient afforestation plans.…”

Discovering Mixture-Based Best Regions of Arbitrary Shapes

“…Spatial mixture patterns. The closest work to our setting is a recently proposed approach for detecting spatial mixture patterns of interest [19]. Its main objective is to identify regions that have significantly high or low mixture of points of different types in a fashion that overcomes two intricate issues in previous studies.…”

“…In that case, the goal is to find the best rectangular region of user-specified width and height that maximizes the number or total weight (or some other monotone objective function) of the points enclosed in it. Moreover, other methods have focused on detecting regions that exhibit interesting spatial mixture patterns [15,19].…”

“…On the other hand, low mixture patterns reveal areas that emphasize on specific activities or functions, such as a business district or a nightlife hotspot. Identifying spatial mixture patterns also has an impact on biodiversity applications; e.g., as pointed out in [19], regions with low mixtures of tree genera have been found to be more vulnerable to various tree diseases.…”

“…A common characteristic of existing approaches for discovering spatial mixture patterns is that they scan the area of study by exhaustively enumerating candidate regions of a certain shape, typically a circle or a square [15,19]. Although this method for candidate enumeration is attractive due to its simplicity, such fixedshape regions may not be well-aligned with the actual, arbitrary shapes of high or low mixture regions that occur in the real world.…”