Integrating ensemble-urban cellular automata model with an uncertainty map to improve the performance of a single model

Abstract

Transition rules are the core of urban cellular automata (CA) models. Although the logistic cellular automata (Logistic-CA) is commonly used for rules extraction, it cannot always achieve satisfactory performance because of the spatial heterogeneity and the inherent complexity of urban expansion. This article presents an ensemble-urban cellular automata (Ensemble-CA) model to achieve better transition rules. First, an uncertainty map that assesses the performance of transition rules spatially was achieved. Then, two auxiliary models (i.e. classification and regression tree, CART; and artificial neural network, ANN), both of which have been stabilized with a Bagging algorithm, were prepared for integration using a proposed self-adaptive -nearest neighbors (-NN) combination algorithm. Thereafter, those unconfident sites were replaced with the ensemble output. This model was applied to Guangzhou, China, for an urban growth simulation from 2003 to 2008. Static validation confirmed that this ensemble framework (i.e. without substitution of uncertain sites) can achieve better performance (0.87) in terms of receiver operating characteristic (ROC) statistics (area under the curve, AUC), and outperformed the best single model (ANN, 0.82) and other common strategies (e.g. weighted average, 0.83). After the substitution of unconfident sites, the AUC of Logistic-CA was elevated from 0.78 to 0.81. Subsequently, two urban growth mechanisms (i.e. pixel- and patch-based) were implemented separately based on the integrated transition rules. Experimental results revealed that the accuracy obtained from simulation of the Ensemble-CA increased considerably. The obtained kappa outperformed the single model, with improvements of 1.74% and 2.76% for pixel- and patch-based approaches, respectively. Correspondingly, landscape similarity index (LSI) improvements of these two mechanisms were 4.24% and 1.82%.

Keywords:

• cellular automata
• bagging
• self-adaptive k-NN
• uncertainty
• ensemble

Acknowledgements

The authors are grateful to anonymous reviewers for their useful comments and suggestions. This research was partially supported by the National High Technology Research and Development Program of China (2013AA122804), the National Science Fund for Excellent Young Scholars (41322009), the National Youth Top-notch Talent Support Program (4109426), and a research grant from Tsinghua University (2012Z02287).