Using a maximum entropy model to optimize the stochastic component of urban cellular automata models

ABSTRACT

The stochastic perturbation of urban cellular automata (CA) model is difficult to fine-tune and does not take the constraint of known factors into account when using a stochastic variable, and the simulation results can be quite different when using the Monte Carlo method, reducing the accuracy of the simulated results. Therefore, in this paper, we optimize the stochastic component of an urban CA model by the use of a maximum entropy model to differentially control the intensity of the stochastic perturbation in the spatial domain. We use the kappa coefficient, figure of merit, and landscape metrics to evaluate the accuracy of the simulated results. Through the experimental results obtained for Wuhan, China, the effectiveness of the optimization is proved. The results show that, after the optimization, the kappa coefficient and figure of merit of the simulated results are significantly improved when using the stochastic variable, slightly improved when using Monte Carlo methods. The landscape metrics for the simulated results and actual data are much closer when using the stochastic variable, and slightly closer when using the Monte Carlo method, but the difference between the simulated results is narrowed, reflecting the fact that the results are more reliable.

KEYWORDS:

• Urban cellular automata
• maximum entropy
• stochastic component
• geographic simulation

Acknowledgments

We fully appreciate Prof. May Yuan, A/Prof. Sytze de Bruin, and the anonymous reviewers for their helpful comments and suggestions.

Data and codes availability statement

The data and codes that support the findings of this study are available in [figshare.com] with the identifier [https://doi.org/10.6084/m9.figshare.10058921.v1].

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [41571384]

Notes on contributors

Haijun Wang

Haijun Wang was a lecturer at Wuhan University from 2003 to 2008, and associate professor from 2008 to 2015. He studied as a visiting scholar at the University of Hong Kong from 2013 to 2014. He is currently a professor and PhD Tutor in the School of Resource and Environmental Sciences at Wuhan University, China. He is mainly engaged in geographical simulation, urban planning and land resource evaluation research.

Bin Zhang

Bin Zhang is a PhD student at School of Resource and Environmental Sciences at Wuhan University, China. His research  interests are geographical simulation and LUCC. He is especially interested in simulating urban expansion using cellular automata models and optimization methods.

Chang Xia

Chang Xia is a PhD student at Department of Urban Planning and Design at University of Hong Kong. He received his master degree in land use management from Wuhan University. His research interests include urban growth modeling and urban landscape analysis.

Sanwei He

Sanwei He is an associate professor from Zhongnan University of Economics and Law, her research interests are urban and regional development.

Wenting Zhang

Wenting Zhang is an associate professor from Huazhong Agricultural University, her research interests are land use simulation and optimization.