Two-stage permutation tests for determining homogeneity within a spatial cluster

ABSTRACT

The discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park’s test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and q-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications.

KEYWORDS:

• Spatial clustering
• permutation test
• homogeneity
• cluster validation

Acknowledgments

The authors gratefully acknowledge the comments from the editor and the reviewers.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Key Research and Development Foundation of China [2017YFB0503601]; National Science Foundation of China (NSFC) [41601410 and 41730105]; The Innovation-Driven Project of Central South University [2018CX015].

Notes on contributors

Qiliang Liu

Qiliang Liu received the Ph.D. degree in geographical information science from The Hong Kong Polytechnic University in 2015. He is currently an associate professor at Central South University, Hunan, China. His research interests  focus on  multi-scale spatio-temporal data mining and spatio-temporal statistics. He has published more than 30 peer-reviewed journal articles in these areas.

Wenkai Liu

Wenkai Liu is currently a Ph.D. candidate at Central South University and his research interests focus on spatio-temporal clustering and association rule mining.

Jianbo Tang

Jianbo Tang received the Ph.D. degree from Central South University and his research interests focus on spatio-temporal clustering and road data updating.

Min Deng

Min Deng is currently a professor at Central South University and the associate dean of School of Geosciences and info-physics. His research interests are map generalization, spatio-temporal data analysis and mining.

Yaolin Liu

Yaolin Liu is currently a Professor at Wuhan University. His research interests include Geographic Information Science, geographic data mining, and spatial analysis and decision making.