Integrating Cellular Automata with the Deep Belief Network for Simulating Urban Growth

Ye Zhou, Feng Zhang, Zhenhong Du, Xinyue Ye, Renyi Liu
2017 Sustainability  
Sustainable urban development is a focus of regional policy makers; therefore, how to measure and understand urban growth is an important research topic. This paper quantified the amount of urban growth on land use maps that were derived from multi-temporal Landsat images of Jiaxing City as a rapidly-growing city in Zhejiang Province from 2000-2015. Furthermore, a new approach coupled the heuristic bat algorithm (BA) and deep belief network (DBN) with the cellular automata (CA) model (DBN-CA),
more » ... hich was developed to simulate the urban expansion in 2015 and forecast the distribution of urban areas of Jiaxing City in 2024. The BA was proposed to obtain the best structure of the DBN, while the optimized DBN model considered the nonlinear spatial-temporal relationship of driving forces in urban expansion. Comparisons between the DBN-CA and the conventional artificial neural network-based CA (ANN-CA) model were also performed. This study demonstrates that the proposed model is more stable and accurate than the ANN-CA model, since the minimum and maximum values of the kappa coefficient of the DBN-CA were 77.109% and 78.366%, while the ANN-CA's values were 63.460% and 76.151% over the 200 experiments, respectively. Therefore, the DBN-CA model is a potentially effective new approach to survey land use change and urban expansion and allows sustainability research to study the health of urban growth trends. change and urban expansion simulation [15] [16] [17] [18] [19] [20] [21] [22] [23] . However, it remains a significant challenge to specify the transition rules of CA. The objective of CA calibration is to obtain the best transition rules that allow for the most accurate simulated results [23, 24] . Consequently, it is crucial to properly calibrate CA parameters to acquire more precise land use change results. So far, a large number of methods has been developed to calibrate CA parameters. Some authors used the SLEUTH urban growth model developed by Clarke based on the cellular automata to simulate urban expansion [16, 17, 25, 26] . However, the input layers of the SLEUTH model are slope, land use/land cover, excluded zones, urban areas, transportation network and hillshading, which do not consider population change and socio-economic development. Furthermore, while the five variable parameters of the SLEUTH independently range from 0-100, there are too many combinations that can influence model performance. Wu (1998) [27], Wu and Webster (1998) [28] defined a multi-criteria evaluation (MCE) method based on the analytic hierarchy process (AHP) to obtain transition rules. Specifically, whether a cell developed or not was determined by the comprehensive evaluation of various spatial variables. Nonetheless, CA calibration with MCE is highly affected by the subjective parameter setting. Therefore, a number of studies proposed a CA model based on logistic regression to deal with multi-factor problems [29, 30] . However, logistic regression is more likely to overfit and has difficulty effectively determining the complex relationships among variables. Consequently, artificial intelligence, machine learning techniques (e.g., support vector machine) and global intelligent optimization algorithms were introduced into CA parameter calibration [22, [31] [32] [33] . Li and Yeh (2002) [18] first integrated artificial neural networks (ANNs) with CA models to simulate land use change. They demonstrated that the ANN-based CA (ANN-CA) model can be successfully applied to land use change and urban expansion simulations, due to ANNs' strong self-adaptiveness, self-organization and ability to learn and mimic complex nonlinear problems [2, 19, 21, 32, 34] . However, the conventional ANNs are weak in global searching and fall more easily into local optima. Hence, improving conventional ANNs or developing a new method to be coupled with the CA might offer better simulation precision. In the past decade, deep learning has shown great success with speech recognition and image classification [35] [36] [37] . As one of the dominant methods of deep learning, the deep belief network (DBN) has excellent feature detection abilities. When compared to the conventional ANNs, the DBN is more capable of interpreting complex mathematical models, due to a number of hidden layers for the feature detection [38] [39] [40] . Furthermore, it is much easier to express the non-linear, complex structures of the data in deep hidden layers. There is a fast, greedy, unsupervised learning algorithm that can initialize the weights of conventional ANN. DBN and ANN both employ a machine learning approach, which is not dependent on fixed functional relationships and is able to handle complex non-linear functions without any a priori knowledge of variable relationships [21, 41] . Thus, the DBN overcomes ANN's local convergence problem effectively. However, so far, only a few studies have combined DBN with the CA model to simulate land use change or urban growth. Typical studies in urban growth used remote sensing and GIS techniques [2, 27, 41, 42] and utilized three phases during model implementation: calibration, validation and prediction. Alsharif and Pradhan used a logistic regression model in the calibration phase from 1984, validation from 2002 and prediction for 2020 and 2025. Grekousis, Manetos and Photis integrated the ANN and fuzzy logic with GIS to calibrate, validate and predict urban growth for the Athens metropolitan area [41] . The ANN model in conjunction with other methods was also used to simulate urban growth including both calibration and validation [44] [45] [46] . Berberoglu, Akın and Clarke compared urban modeling approaches, including logistic regression, regression tree, ANN and SLEUTH, to forecast the urban growth, and two calibration and prediction phases of these models were performed [47] . Riccioli utilized CA and Markov chains to examine the land use changes from 1990-2000, and it was validated for 2006 [48] . In this context, our research aims to propose a DBN-based CA (DBN-CA) model to simulate the spatial-temporal changes in non-urban land use, while the metaheuristic bat algorithm (BA) developed
doi:10.3390/su9101786 fatcat:4mhtehhwkzc5fem3gwkmx23awu