L-function of geographical flows

ABSTRACT

Geographical flow (hereafter flow) can be modeled as an orderly connected point pair composed of an origin (O) and a destination (D). Aggregation is the most common form of spatial heterogeneity of flows, which we define as their deviation from complete spatial randomness (CSR), and the aggregation scale is an important indicator for its perception. Nevertheless, quantifying the aggregation scale of flows is still an unsolved problem. In this paper, we propose the L-function for flows as a solution, derive theoretical null models of the K-function and L-function in a flow space. We conduct simulation experiments to validate the L-function and its capability to detect aggregation scales. Finally, we apply the solution in a case study with taxi data in Beijing and identify nine aggregation scales of taxi OD flows, ranging from 170 m to 22.1 km. These scales correspond to three classes: less than 300 m, from 600 m to 700 m and more than 1500 m. The classes are related to the sizes of the urban facilities where the dominant flow clusters occur, indicating that the L-function in flow space can detect the aggregation scale of flows at the building scale, the block scale and the district scale.

KEYWORDS:

• Flow space
• aggregation scale
• Ripley’s L-function
• origin-destination flow
• spatial statistics

Acknowledgments

The authors thank the editor and the anonymous reviewers for their helpful comments on an earlier draft of this paper.

Data and codes availability statement

The data and codes that support the findings of this study are available in ‘figshare.com’ with the identifier(s): https://doi.org/10.6084/m9.figshare.12005385.v1

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 41525004, 41421001) and the National Key R&D Program of China (Grant No. 2017YFB0503604).

Notes on contributors

Hua Shu

Hua Shu is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial statistics and spatial big data mining about human movements in the city.

Tao Pei

Prof. Tao Pei is a professor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial big data mining and geostatistics.

Ci Song

Dr. Ci Song is an assistant professor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial data mining, spatial analysis, and geographic information science.

Xiao Chen

Xiao Chen is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. Her research interests include spatial statistics, spatial analysis, and spatial big data mining.

Sihui Guo

Sihui Guo is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. Her primary research interest is in the area of geographical big data mining. She is currently working on the flow pattern mining in cities.

Yaxi Liu

Yaxi Liu is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial-temporal data mining, mobile computing, and geographic information science.

Jie Chen

Dr. Jie Chen is an assistant professor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial big data mining and urban computing.

Xi Wang

Xi Wang is a doctoral candidate at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial data mining and social computing.

Chenghu Zhou

Prof. Chenghu Zhou is a professor at the Institute of Geographical Sciences and Natural Resources Research, CAS. His research interests include spatial data mining, intelligent computation in geosciences and geoscientific analysis of remote sensing images.