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Given a collection of Boolean spatial feature types, their instances, a neighborhood relation (e.g., proximity), and a hierarchical taxonomy of the feature types, the goal is to find the subsets of feature types or their parents whose spatial interaction is statistically significant. This problem is for taxonomy-reliant applications such as ecology (e.g., finding new symbiotic relationships across the food chain), spatial pathology (e.g., immunotherapy for cancer), retail, etc. The problem is computationally challenging due to the exponential number of candidate co-location patterns generated by the taxonomy. Most approaches for co-location pattern detection overlook the hierarchical relationships among spatial features, and the statistical significance of the detected patterns is not always considered, leading to potential false discoveries. This paper introduces two methods for incorporating taxonomies and assessing the statistical significance of co-location patterns. The baseline approach iteratively checks the significance of co-locations between leaf nodes or their ancestors in the taxonomy. Using the Benjamini-Hochberg procedure, an advanced approach is proposed to control the false discovery rate. This approach effectively reduces the risk of false discoveries while maintaining the power to detect true co-location patterns. Experimental evaluation and case study results show the effectiveness of the approach. 

Given a set S of spatial feature types, its feature instances, a study area, and a neighbor relationship, the goal is to find pairs such that C is a statistically significant regional-colocation pattern in r_{g}. This problem is important for applications in various domains including ecology, economics, and sociology. The problem is computationally challenging due to the exponential number of regional colocation patterns and candidate regions. Previously, we proposed a miner [Subhankar et. al, 2022] that finds statistically significant regional colocation patterns. However, the numerous simultaneous statistical inferences raise the risk of false discoveries (also known as the multiple comparisons problem) and carry a high computational cost. We propose a novel algorithm, namely, multiple comparisons regional colocation miner (MultComp-RCM) which uses a Bonferroni correction. Theoretical analysis, experimental evaluation, and case study results show that the proposed method reduces both the false discovery rate and computational cost. 

Mapping of spatial hotspots, i.e., regions with significantly higher rates of generating cases of certain events (e.g., disease or crime cases), is an important task in diverse societal domains, including public health, public safety, transportation, agriculture, environmental science, and so on. Clustering techniques required by these domains differ from traditional clustering methods due to the high economic and social costs of spurious results (e.g., false alarms of crime clusters). As a result, statistical rigor is needed explicitly to control the rate of spurious detections. To address this challenge, techniques for statistically-robust clustering (e.g., scan statistics) have been extensively studied by the data mining and statistics communities. In this survey, we present an up-to-date and detailed review of the models and algorithms developed by this field. We first present a general taxonomy for statistically-robust clustering, covering key steps of data and statistical modeling, region enumeration and maximization, and significance testing. We further discuss different paradigms and methods within each of the key steps. Finally, we highlight research gaps and potential future directions, which may serve as a stepping stone in generating new ideas and thoughts in this growing field and beyond. 

Given a set S of spatial feature types, its feature instances, a study area, and a neighbor relationship, the goal is to find pairs such that C is a statistically significant regional-colocation pattern in r_{g}. This problem is important for applications in various domains including ecology, economics, and sociology. The problem is computationally challenging due to the exponential number of regional colocation patterns and candidate regions. Previously, we proposed a miner [Subhankar et. al, 2022] that finds statistically significant regional colocation patterns. However, the numerous simultaneous statistical inferences raise the risk of false discoveries (also known as the multiple comparisons problem) and carry a high computational cost. We propose a novel algorithm, namely, multiple comparisons regional colocation miner (MultComp-RCM) which uses a Bonferroni correction. Theoretical analysis, experimental evaluation, and case study results show that the proposed method reduces both the false discovery rate and computational cost.