Norma: A Framework for Finding Threshold Associations Between Continuous Variables Using Point-wise Functions

This paper introduces Norma, a novel association analysis framework for continuous spatial variables. Unlike other point-based spatial analysis methods, Norma associates a point-wise function with each continuous variable-e.g., a function that returns poverty rates for each location in New Mexico, and then finds interesting associations between continuous variables by analyzing relationships between the respective point-wise functions. Moreover, the paper introduces a new association called Continuous Variable Threshold (CVT) pattern, aiming to identify a pair of thresholds within the domains of two continuous variables which exhibit strong associations within an observation area. For example, it may unveil a strong association between COVID-19 infection rates above 2% and poverty rates above 15% in New Mexico. To find such associations, Norma employs a novel interestingness function, which measures agreement with respect to hotspots where each point-wise function exceeds the associated threshold. To be able to compute such hotspots, the paper proposes a novel grid-based spatial hotspot-growing algorithm which computes regions of a point-wise function above a given threshold. Furthermore, Norma introduces a measure area under the curve (AUC) for assessing variable relatedness based on observed CVT associations and an algorithm to determine the AUC in 2D space. Finally, the results of a comparative case study are presented which uses county-level COVID-19 infection rates and nineteen socio-economic variables from the contiguous United States which demonstrates the merit of Norma’s association analysis approach.