Flow Cross K-function: a bivariate flow analytical method

ABSTRACT

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.

KEYWORDS:

• Flow data
• spatial statistics
• bivariate
• taxi trips
• spatial competition

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental material

Supplemental data for this article can be accessed on the here.

Additional information

Notes on contributors

Ran Tao

Ran Tao is an assistant professor at the University of South Florida. Tao's research centers on GIScience methods and applications. He is particularly interested in studying spatial interaction phenomena such as movement, migration, and even information flows in the virtual world. He has developed a series of flow data analytical methods that blend the latest techniques in spatial statistics, data mining, geovisualization, and geocomputation. He is leading or actively engaged in collaborative research projects which exert the power of his methods to a variety of domains, such as studying intracity movement behavior in metropolitan areas in the U.S., investigating shrinking city phenomena in Northeast China with intercity migration data, and modeling territorial control based on violent conflict events in Sub-Saharan Africa.

Jean-Claude Thill

Jean-Claude Thill is Knight Distinguished Professor of Public Policy at the University of North Carolina at Charlotte. For three decades, he has developed his scholarship in computational social sciences, particularly emphasizing the spatial and regional perspective. In this perspective, place matters and location is a critical element in how socio and economic structures organize and behave. His research distinctively brings cutting-edge modeling techniques to support public policy framing.