Flow Cross K-function: a bivariate flow analytical method

Spatial flow data represent meaningful interaction activities between pairs of corresponding locations, such as daily commuting, animal migration, and merchandise shipping. Despite recent advances in flow data analytics, there is a lack of literature on detecting bivariate or multivariate spatial flow patterns. In this paper we introduce a new spatial statistical method called Flow Cross K-function, which combines the Cross K-function that detects marked point patterns and the Flow K-function that detects univariate flow clustering patterns. Flow Cross K-function specifically assesses spatial dependence of two types of flow events, in other words, whether one type of flows is spatially associated with the other, and if so, whether this is according to a clustering or dispersion trend. Both a global version and a local version of Flow Cross K-function are developed. The former measures the overall bivariate flow patterns in the study area, while the latter can identify anomalies at local scales that may not follow the global trend. We test our method with carefully designed synthetic data that simulate the extreme situations. We exemplify the usefulness of this method with an empirical study that examines the distributions of taxi trip flows in New York City.