Supporting SLEUTH – Enhancing a cellular automaton with support vector machines for urban growth modeling

Highlights

• Creation of probability maps for urban growth derived by support vector machines and binary logistic regression.

• Coupling of a modified version of SLEUTH and binary logistic regression resp. support vector machines.

• Simulation of urban growth between 1975 and 2005 in the southern part of North-Rhine Westphalia.

• Examination of a probable enhancement of SLEUTH by using various validation techniques with different foci of analysis.

Abstract

In recent years, urbanization has been one of the most striking change processes in the socioecological system of Central Europe. Cellular automata (CA) are a popular and robust approach for the spatially explicit simulation of land-use and land-cover changes. The CA SLEUTH simulates urban growth using four simple but effective growth rules. Although the performance of SLEUTH is very high, the modeling process still is strongly influenced by stochastic decisions resulting in a variable pattern. Besides, it gives no information about the human and ecological forces driving the local suitability of urban growth. Hence, the objective of this research is to combine the simulation skills of CA with the machine learning approach called support vector machines (SVM). SVM has the basic idea to project input vectors on a higher-dimensional feature space, in which an optimal hyperplane can be constructed for separating the data into two or more classes. By using a forward feature selection, important features can be identified and separated from unimportant ones. The anchor point of coupling both methods is the exclusion layer of SLEUTH. It will be replaced by a SVM-based probability map of urban growth. As a kind of litmus test, we compare the approach with the combination of CA and binomial logistic regression (BLR), a frequently used technique in urban growth studies. The integrated models are applied to an area in the federal state of North Rhine-Westphalia involving a highly urbanized region along the Rhine valley (Cologne, Düsseldorf) and a rural, hilly region (Bergisches Land) with a dispersed settlement pattern. Various geophysical and socio-economic driving forces are included, and comparatively evaluated. The validation shows that the quantity and the allocation performance of SLEUTH are augmented clearly when coupling SLEUTH with a BLR- or SVM-based probability map. The combination enables the dynamical simulation of different growth types on the one hand as well as the analyses of various geophysical and socio-economic driving forces on the other hand. The SVM approach needs less variables than the BLR model and SVM-based probabilities exhibit a higher certainty compared to those derived by BLR.

Introduction

In recent years, urbanization has become one of the most striking change processes in the coupled human-environment system of Central Europe (Antrop, 2004, Siedentop, 2006). The quantitative and qualitative measurement, prediction, and evaluation of land-use dynamics – especially urban sprawl – have come to play a central role in land-system science (Brown et al., 2004, Lambin and Geist, 2006, Verburg, 2006). The creation of appropriate and adjusted models is challenged by the complexity of urban systems with their manifold self-organization processes, non-linear relationships, and emergent properties as well as feedback loops between different spatio-temporal scales and compartments. In this context, an increasing number of studies testing the use of artificial intelligence techniques for urban simulation have emerged recently (Batty, 2005, Benenson and Torrens, 2004, Schwarz and Haase, 2007, Steven et al., 2002, Wu and Silva, 2010).

Among these popular techniques are spatially explicit cellular automata (CA) like SLEUTH (Clarke, Hoppen, & Gaydos, 1997). SLEUTH is an acronym for its suite of input data (Slope, Land use, Exclusion, Urban, Transportation, and Hillshade) and is a purely growth-oriented model. As a bottom-up approach it is not dependent on intensive preliminary studies regarding the general causes of urban growth in a study area or the location-specific driving forces (Clarke et al., 1997). Based on the principles of neighborhood effects and spatial autocorrelation, the simulation rules are relatively simple. However, due to its ability to capture the complex emergence of urban patterns, SLEUTH has been applied in several urban growth studies throughout the world (Chaudhuri and Clarke, 2013, Clarke et al., 1997, Rafiee et al., 2009, Silva and Clarke, 2005, Wu et al., 2008). Although SLEUTH can simulate urban growth quite accurately, the modeling process is strongly influenced by stochastic decisions, resulting in variable growth patterns (Chaudhuri & Clarke, 2013). Nor does SLEUTH provide information regarding important human and ecological forces which determine the local suitability of urban growth.

The machine learning concept called support vector machines (SVM) (Cortes & Vapnik, 1995) is able to overcome these disadvantages. SVM are used in a variety of applications for solving classification problems (Drucker et al., 1999, Guo et al., 2005, Mountrakis et al., 2011, Waske et al., 2010) and for regression challenges (Gestel et al., 2001, Verplancke et al., 2008). In SVM explanatory variables are used to calculate probabilities for specified conditions (e.g. a raster cell belonging to a specific class). Conceptually in SVM, input vectors are projected in a higher-dimensional feature space in which an optimal hyperplane can be constructed for separating the input data into two or more classes. By using a specific feature selection, significant features can be identified and separated from those which are not of interest. In this manner, insights may be gained into those characteristic features which determine the separation process.

Xie (2006) implemented SVM for general land-use change objectives and tested different modification possibilities. Huang, Xie, and Tay (2010) extended the results of SVM for rural–urban simulation applications. A spatially explicit application with the purpose of dynamic modeling of urban growth is not performed and neither is a feature selection conducted to analyze the different impacts of the possible driving factors. Yang, Li, and Shi (2008) and Okwuashi, McConchie, Nwilo, and Eyo (2009) combined SVM with CA-based approaches for modeling urban growth in a spatially explicit way. Yang et al. (2008) applied their model to Shenzen city; Okwuashi et al. (2009) modeled the Lekki area of Lagos. Both of these studies derived nonlinear transition rules for CA simulation of urban land-use dynamics, but did not exploit the complementary advantages of SVM and CA. In both of these cases, urban growth was erroneously directed. As a result, the predicted growth of beaches and aquacultures was artificially limited (Yang et al., 2008) or urban edge growth was overestimated (Okwuashi et al., 2009). In addition, these two studies examined only common proximity and market access distance variables, while other important growth stimuli such as demographic changes or fluctuations in regional job markets were not considered.

This previous work has led us to the principal objective of this research: to combine the simulation strengths of SLEUTH and SVM. We focus on this objective by using an SVM-based probability map where geophysical and socio-economic forces drive the local suitability of urban growth (Mountrakis et al., 2011, Waske et al., 2010). We then compare the results with a combination of SLEUTH and binomial logistic regression (BLR – Lesschen et al., 2005, Verburg et al., 1999). Two primary research questions of this study are:

• Can the performance of SLEUTH be enhanced by using an SVM-based probability map?

• How well do SVM perform in comparison to the widely used BLR in an urban growth application?

The paper is structured as follows: Following this Introduction, Section 2 describes our study area as well as the compilation of the various input data sets. In Section 3 we detail the applied models and the chosen methods for assessing their accuracy. Section 4 presents an analysis of the selected driving forces, along with the derived probability maps and discusses the validation results. Finally, Section 5 provides a short conclusion and offers a perspective for future research.