cover changes by RBFN-based CA model

cover changes by RBFN-based CA model

Computers & Geosciences 37 (2011) 111–121 Contents lists available at ScienceDirect Computers & Geosciences journal homepage: www.elsevier.com/locat...

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Computers & Geosciences 37 (2011) 111–121

Contents lists available at ScienceDirect

Computers & Geosciences journal homepage: www.elsevier.com/locate/cageo

Simulating multiple class urban land-use/cover changes by RBFN-based CA model Yang Wang, Shuangcheng Li n College of Urban and Environmental Sciences, Peking University, The Key Laboratory for Earth Surface Processes, Ministry of Education, 100871 Beijing, China

a r t i c l e in f o

abstract

Article history: Received 24 April 2009 Received in revised form 25 April 2010 Accepted 18 July 2010 Available online 7 November 2010

Land use systems are complex adaptive systems, and they are characterized by emergence, nonlinearity, feedbacks, self organization, path dependence, adaptation, and multiple-scale characteristics. Land use/ cover change has been recognized as one of the major drivers of global environmental change. This paper presents a coupled Cellular Automata (CA) and Radial Basis Function Neural (RBFN) Network model, which combines Geographic Information Systems (GIS) to contribute to the understanding of the complex land use/cover change process. In this model, GIS analysis is used to generate spatial drivers of land use/ cover changes, and RBFN is trained to extract model parameters. Through the RBFN-CA model, the conversion probabilities of each cell from its initial land use state to the target type can be generated automatically. Future land use/cover scenarios are projected by using generated parameters in the model training process. This RBFN-CA model is tested based on the comparison of model output and the real data. A BPN-CA model is also built and compared with the RBFN-CA model by using a variety of calibration metrics, including confusion matrix, figure of merit, and landscape metrics. Both the location and landscape metrics based assessment for model simulation indicate that the RBFN-CA model performs better than the BPN-CA model for simulating land use changes in the study area. Therefore the RBFN-CA model is capable of simulating multiple classes of land use/cover changes and can be used as a useful communication environment for stakeholders involved in land use decision-making. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Cellular Automata Radial Basis Function Neural Network Computer Simulation GIS Spatial Analysis Shenzhen City China

1. Introduction Land use and cover changes are critical to the research of the Global Land Project (GLP), which aims to measure, model, and understand the coupled human-environmental system as part of broader efforts to address changes in earth processes and subsequent human consequences (Global Land Project 2005). Changes in land use result from interaction among social systems, ecological dynamics, and land management (Turner et al., 2007). They also affect the states, properties, and functions of ecosystem at both local and globe scale (Foley et al., 2005; Liu et al., 2007). Interdisciplinary research and computational models are increasingly important to understanding the complexity of land use/cover change (LUCC) processes. They tend to blend an array of data, methods, and theories. Models can help provide the conceptual and methodological integration necessary for interdisciplinary research. Modeling methodologies range from simple mathematic formulas to intricate spatiotemporal simulations (Manson, 2005).

Some of the earliest formal models of land use change were equilibrium models of the economics of land use. Models ¨ of land use changes, of the type developed by Von Thunen and Ricardo, are well established in the geography, regional science, economics, and urban planning literatures (Alonso, 1964; Fajita, 1982). The general approach was to establish land rents for urban land use on the basis of location relative to a city center and other factors (Alonso, 1964). Most of these models are limited to relatively static conditions and are therefore not suited to exploring the roles of feedbacks and path dependence on land use change processes. To model land use/cover change more dynamically, spatially explicit models, including GEOMOD (Pontius et al., 2001, 2005), SLEUTH (Silva and Clarke, 2002), CLEU (de Koning et al., 1999; Verburg et al., 2002; Verburg and Veldkamp, 2005), LTM (Pijanowski et al., 2002, 2005) and MAS (Brown et al., 2005) have been developed. They typically begin with a digital map of an initial time and then simulate transitions in order to produce a prediction map for a subsequent time (Pontius et al., 2008).

 Cellular Automata (CA) models are common in the land use

n

Corresponding author. Tel.: + 86 106 276 7428; fax: + 86 1062 751 187. E-mail address: [email protected] (S. Li).

0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cageo.2010.07.006

modeling literature (Batty and Xie, 1994; Batty et al., 1997; Clarke and Gaydos, 1998). They were originally conceived by Ulam and Von Neumann in 1940s to provide a formal framework for investigating the behavior of complex, extended

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Fig. 1. Location of study area.

system. Cellular Automata were defined by (a) a spatial grid or tessellation of cells; (b) a finite set of state which each grid cell can assume; (c) an initial state configuration of the whole grid; and (d) rules that define transitions between cell states (Clarke and Gaydos, 1998; White and Engelen, 2000). That means the model’s decision concerning whether to change the state of a cell takes into consideration explicitly the state of the neighboring cells. In land use modeling, the cells represent parcels of land, each with its own characteristics (quality, usage), and each changing as a result of neighborhood functions.

Artificial neural networks (ANNs) are powerful tools that use the machine learning approaches to quantify and model complex behavior and patterns (Pijanowski et al., 2002). The first ANNs, developed by Rosenblatt, receive weighted inputs and thresholds according to a defined rule to classify linearly separable data through linear functions. Updated network types, like the Multilayer Perceptron (MLP), Radial Basis Function (RBF), Kohonen SelfOrganizing Map (Kohonen), and so on, are widely used on nonlinear phenomena. There are input layers, hidden layers, and output layers in these networks in general (Dai et al., 2005). Neural net calculate weights for input layer nodes, hidden layer nodes, and output layer nodes, by introducing the input in a feed forward manner throughout the network layers. Weights in a neural network are incrementally modified so as to improve a prespecified performance criterion by using a training algorithm (Hassoun, 1995). Some researchers (Torrens and Benenson, 2005; Torrens, 2009) consider ANN and CA to belong to the same family of models and at times do not make much distinction between them. The parent models can be called computing automata, the basic structure of which may be characterized as follows: A  ðS,RÞ; S ¼ fS1 ,S2 ,. . .,Sk g;

R : ðSt ,It Þ-St þ 1 :

ð1Þ

where A represents an automaton, characterized by states S and a transition rule T. The transition rule functions to manage changes in states S from time t to time t +1, given input of other state information from outside the automaton at time t.

Examples of computing automata include finite state machines, turing machines, and artificial neural networks. The input layer in a neural network can be considered as the state St, while the output layer is considered as St + 1. Cellular automata add an additional characteristic to the above automaton: the notion that automata can be considered as being housed discretely within the confines of a cellular unit. Adding cells to the basic automaton structure yields the following specification. CA  ðS,T,NÞ; S ¼ fS1 ,S2 ,. . .,Sk Þ;

R : ðSt ,Nt Þ-St þ 1

ð2Þ

where CA refers to a cellular automaton, characterized by states S, a transition rule (or vector of rules) R, and a neighborhood N. The transition rules may be formulated as functions, operators, mappings, expressions, or any mechanism that describes how an automaton should react to input. This paper provides a Radial Basis Function Neural Network (RBFN) based CA model to simulate multiple-classes of land use/ cover changes in Shenzhen City, Guangdong province, China. RBFNs were trained to extract land use transition rules, while geographic information systems (GIS) were used to develop the spatial predictor drivers and performed spatial analysis on the results. This RBFN-CA model was tested based on the comparison of model output and real data in the period 2000–2005. A BPN-CA model was also built and compared with the RBFN-CA model by using a variety of calibration metrics, including confusion matrix, figure of merit, and landscape metrics. Finally, future land use/cover scenarios were forecasted using the RBFN-CA model.

2. Study area and data 2.1. Study area The study area, Shenzhen City, is located in the Guangdong province, China (see Fig. 1). She has 6 districts and covers approximately 1952 km2. Since government of China designated Shenzhen as a special economic zone in 1979, the area has conglomerated nearby small rural towns and villages with less than 20,000 people into a metropolitan area of 8.27 million people. The rapid population growth has resulted in dynamics of landscape

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structures, the most obvious type of which is built up areas increasing, while farmland, forests, and grasslands decreasing (Sui and Zeng, 2001). The degree of transformation of land use from 1985 to 1995 was greater than that from 1995 to 2005, because of some effective measures taken by the national and local governments to restore the environment and to preserve natural resources in the later period (Dai et al., 2005).

2.2. Data To simulate changes of the complex urban land use system, two high resolution remote sensing data sets were needed. In this study, 2000 and 2005 Landsat Thematic Mapper (TM) images were used as empirical data to reveal the rapid land use conversions. Conventional image preprocessing, including image enhancement, geometric correction, georeferencing, classification and information extraction

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were performed for these two images. The whole experimental data were classified into seven types, i.e. forest, orchards, cropland, built up areas, unused areas, water, and beach. In general, the conversions of land use types are influenced by a series of spatial variables in terms of accessibility or proximity e.g. distances to urban centers, town centers and transportation lines (Li and Yeh, 2002). Some vector traffic maps were used to provide the spatial information, such as urban centers, county centers, and administrative boundaries. Other physical factors including slope and elevation were derived from a Digital Elevation Model (DEM). To ensure consistency of the data, all images or maps were geometrically rectified with each other and subsequently referenced to the Albers Equal Area project system, with the central meridian 1051E, first standard parallel 251N, and second standard parallel 471N. Land use types and other spatial GIS data used for simulating were converted to an Arc/INFO GRID format, and then resampled to a spatial resolution of 100 m  100 m to match DEM data. Fig. 2 represents the two images after GIS processing. For this

Fig. 2. Land use classification in 2000 and 2005. The whole experimental data were classified into seven types, i.e. cropland, orchards, beach, built up areas, unused areas, forest, and water.

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study area, a total of 191.03 thousands cells were included in the modeling exercise, with 947 columns and 570 rows. Table 1 shows the statistical data of land use patterns in 2000 and 2005.

Table 1 Land use structures in 2000 and 2005. 2000

2005

Land use types

Proportion (%)

Land use types

Proportion (%)

forest orchard farmland built up areas unused areas water beach

37.84 17.63 3.00 23.21 9.26 1.71 7.35

forest orchard farmland built up areas unused areas water beach

24.77 23.61 1.23 34.83 9.67 1.72 4.17

3. Methods and analytical procedures 3.1. GIS analysis In this study, we used GIS to process data for input to the artificial neural network. Euclidean distances were calculated and stored in separate Arc/INFO GRID files. The distance each cell in the entire environment from the railways, highways, and county roads represent the potential accessibility of a location for new development. These distance features serve to either improve the access of the site to urban areas (i.e. county road, railways, and highways) or to increase the suitability of a site to develop (Pijanowski et al., 2002). Tobler (1970) stated that ‘‘Everything is related to everything else, but near things are more related than distant things’’. Translated into a land use context implies that the surrounding of a location are related to the land use at that location, but close

Fig. 3. Spatial variables used for network training exercise.

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surroundings have a stronger influence than more remote surroundings (Vliet et al., 2009). With some simple local rules, cellular automata provide an effective way for modeling the complex land use changes. Moreover, they are inherently spatial and their structures are compatible with geospatial data. In GIS environment, spatial GRID files can serve as cellular space, in which each grid is regarded as a cell with unique attributes, while vector data can provide the distance attributes. Neighborhood functions are central to the CA models (Li and Yeh, 2002). In land use changes, the neighborhood effect represents attraction or repulsion of neighboring land use types. The definition of the neighborhood has a significant impact on the transition rules, since the scope that center cellular influences will be determined by the size of the neighborhood. In this paper, a 7  7 window was used the count the average value of each land use type in the neighborhood. Neighborhood variables were obtained through the focal statistic functions in GIS spatial analysis tools. Although neighborhood functions and spatial variables are important for the simulation of multiple classes of land use/cover changes, physical properties such as the soil type and slope should not be neglected. Pijanowski et al. (2002) found that landscape topography was an influential factor contributing toward residential use. Thus, driving variable (i.e. slop) was created from Digital Elevation Model (DEM) using Surface Analysis. Consequently, all spatial variables needed were prepared using GIS analysis tools (see Fig. 3). Here, a GIS database, which contains distance variables, neighborhood variables, and physical variables was built to provide basic spatial information.

3.2. Artificial neural network model 3.2.1. Artificial neural networks Analogous to biological neurons, an artificial neural network consists of a network of partially connected processing elements, units or nodes, arranged in layers (Hassoun, 1995; Tettamanzi and Tomassini, 2001; Arce-Medina and Paz-Paredes, 2009). Each neuron or layer in ANNs represents specific variable or matrix. Unlike human brains, which basically learn from experience, ANNs learn the relations between selected inputs and outputs through an iterative process called training. Training by a neural network implies an adaptive procedure in which the weights of the network which connect different neurons are incrementally modified so as to improve a prespecified performance criterion i.e., an objective function over time (Hassoun, 1995). According to the learning methods, neural networks can be divided into supervised learning networks and unsupervised learning networks. The supervised learning process consists in updating the weights at each training step so that for a given input, an error measure the network’s output and the known target values is reduced (Tettamanzi and Tomassini, 2001). This is also known as learning with a teacher or associative learning. In unsupervised learning there is no feedback which indicates whether a given association is correct or not, in other words, there is no ‘‘teacher’’. Instead, the network itself must be able to discover any categories, patterns, or features possibly hidden in the data. The back propagation (BP) algorithm is by far the most popular method for performing supervised learning of feed forward networks. In BP algorithm, error back propagation is essentially a search procedure that attempts to minimize a whole network error function such as the mean square error (MSE) of the network output over an ensemble of training input/output pairs E ¼ 1=2

m X j¼1

ðdj yj Þ2

ð3Þ

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where dj is the desired jth output and yj is the actual jth output of the network. However, recent contributions in neural network (NN) development and experimentation have pointed that the implement of BPNs often produce some difficulties from the nature of randomness in the initial weight distribution (Ros et al., 2007). Firstly, the neural net could become trapped in a local minima solution that will eventually produce poor results. Secondly, the standard back propagation algorithm might spend more time for training. Radial Basis Function Networks (RBFNs) are recently adopted widely for complex system modeling because they possess simple structure, good local approximating performance, particular resolvability, and function equivalence with a simplified class of fuzzy inference systems (Li and Hori, 2006). Standard Radial Basis Functions (RBF) nets comprise a hidden layer of RBF nodes and an output layer with linear nodes (Broomhead and Lowe, 1988; Moody and Darken, 1989). RBFN is a network that has both supervised and unsupervised learning algorithms. In the unsupervised phase, input data are clustered, and cluster details are sent to hidden neurons, where radial basis functions of the inputs are computed by using the center and the standard deviation of the clusters (Kumar et al., 2008). In the supervised phase, the weights that connect the hidden and output layers are determined. Although RBFNs belong to forward networks because of their structure, the method for initializing parameters is different from the BPNs, in which parameters are initialized randomly. The parameters of RBFN such as the center and width of receptive fields are determined according to the distribution of sample data. In this paper, a three-layer Radial Basis Function Network (RBFN) was designed based on the analysis of RBFNs. Gaussian function was chosen as the active functions of the hidden layer nodes.

ji ðXÞ ¼ exp½99XCi 992 =d2 , i ¼ 1,. . .,n

ð4Þ

where X is an N-dimensional input vector, Ci is a vector (i.e., the center of the Gaussian function) with the same dimension as X, n is

Fig. 4. Flowchart of artificial neural network model for simulating multiple class land use changes.

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the number of nodes in the hidden layer, and di is the width of the Gaussian function. Neurons in the hidden layers perform two tasks: they measure the similarity between the network input nodes and the receptive unit center vector and pass the result through a non-line activation function to the output neuron or adjacent neuron of the corresponding hidden layer (Powell, 1987). The overall output of the RBFN can be computed by using different algorithms. In this study, we used weighted sum of the kernel levels as the network output function. y¼

n X ðri  wi Þ

Comparing the target and calculated output values across all observations, errors were determined as follows: E¼

m X

ðyj dj Þ2

ð6Þ

j¼1

where yj and dj indicate the prediction from the jth output unit and the actual measurement given to that neuron, E is typically minimized by the gradient descent algorithm. The resulting weight update rule called the delta rule was expressed as Wij ðkþ 1Þ ¼ Wij ðkÞ þ aðyj dj Þoi

ð7Þ

ð5Þ

1

where ri is the ith output of the hidden layer, w is the weights between the hidden layer neurons and output layer neurons.

where Wij represents the connection weight between the ith hidden neuron and jth output neuron, oi denotes the output from the ith hidden neuron, the remaining a is the learning rate which is set to 0.5 in this study.

Fig. 5. Comparison between simulated land use patterns in 2005 by using RBFN-CA model and BPN-CA model.

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3.2.2. Training Each single record consisting of input and output variables in the GIS can be regarded as a pattern. The network finds patterns associate the given input with desired output. In this paper, the input vector X were values assigned to cells based on local and physical characteristic such as distance variables, neighborhood variables, natural attributes. Before training, all input data were normalized between 0 and 1. The scaling of variable values is to avoid using data spanning over different orders of magnitude. The transformation was carried out by xiuðk,tÞ ¼

xi ðk,tÞmin maxmin

ð8Þ

where xi(k,t) is the measured value applied to variable i, x0 i(k,t) is the respective normalized value for the variable. In this model, there were thirteen neurons in the input layer corresponding to the number of spatial variables. The target output values were set to seven numbers, where the number 1 represented the target land use type in 2005. The ‘‘change likelihood value’’, which specifies the relative likelihood for each cell was stored as the produced output. The range of the produced output values was from 0 (‘‘no readiness’’ to change into the desired land use type) to 1(the ‘‘highest readiness’’ to change into the target land use type). The method for cell sampling was proportional stratified sampling. It is better than purely random sampling, which may leave out some smaller categories thus making the training data unreasonable (Li and Yeh, 2002). To improve the model generalization, not all the cells were chosen to train the structure of network. A total of 10,000 sampling points were selected in training period, which were divided into training subset and testing subset. Based on the proportion of different land use types in 2000, the corresponding numbers of cells were randomly selected from the pool of available cells and then were presented to the network in random order.

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After all land use influencing factors were incorporated into the RBFN model, transition probabilities of each cell from the existing type to the future ones can be obtained. We followed Pijanowski et al. (2002, 2005) to calibrate the model by threshold setting. Through the comparison between the output values and the threshold, the future land use type of each cell can be determined. That means when the calculated value is bigger than the threshold value (0.5 in this paper), changes will take place, vice versa. Based on the above analysis, we also built a BPN model with the structure of 13  9  7 for a comparison. MATLAB R2008a was utilized for neural network designing and training. We allowed the neural network to train on the input and output data for 4000 cycles till the overall mean squared error generated to be stabilized. 3.2.3. Simulation The process of study was divided into three steps (Fig. 4). In the first step, multiple classes of land use variables were extracted; normalized function of these variables was made; and training data of neural networks were obtained. In the second step, using the extracted variables as an input, the network models were trained in order to obtain the optimal network structures and parameters. Lastly, the near future land use state was projected based on the transition rules and well trained networks. We used all driving variables in 2000 as input of neural network models to calculate transition probabilities of each cell. Depending on the outputs of both BPN and RBFN, simulation of land use types in 2005 can be created and imported into GIS for display and Table 2 An example of a two-dimensional confusion matrix. Actual

Negative Positive

Fig. 6. Projected land use patterns in 2010 by using RBFN-CA model.

Projected Negative

Positive

a c

b d

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analysis. Fig. 5 denotes the results of simulating of multiple classes of land use/cover changes in the period of 2000–2005 by using the land use data in 2000 as the initial grids.

Future projections can be made for each 5-year time step, assuming the development trends remain constant with observed 5-year period. Using spatial variables of 2005 as the input data layers and the same structure of RBFN-CA model, one can get the conversion probabilities from the existing land use state to the ones of 2010 (Fig. 6). 3.2.4. Model goodness of fit A variety of method including confusion matrix, figure of merit, and landscape metrics were applied to assess model performance. A confusion matrix, which contains information about actual and predicted classifications, was done by a classification system. It is appropriate for methods of classification where it is assumed that pixels at the reference locations can be assigned to single classes, and accuracy measures based on the proportion of area correctly classified are then calculated from the number of pixels that are correctly classified (Lewis and Brown, 2001). A typical twodimensional confusion matrix was shown in Table 2. The accuracy is the proportion of the total number of predictions that were correct. It is determined using the following equation: Accuracy ¼ ða þ dÞ=ða þ b þc þ dÞ

ð9Þ

The figure of merit is the ratio of the intersection of the observed change and predicted change to the union of the observed change and predicted change (Pontius et al., 2008). Its value can range from 0%, meaning no overlap between observed and predicted change, to 100%, meaning perfect overlap between observed and predicted change, i.e. a perfectly accurate prediction. Figure of Merit ¼ B=ðA þ B þ C þDÞ,

Fig. 7. Cells by rules of change in period of 2000–2005 (observed, RBFN-CA simulated, BPN-CA simulated).

ð10Þ

where A is area of error due to observed change predicted as persistence, B is area of correct due to observed change predicted as change, C is area of error due to observed change predicted as wrong gaining category, D is area of error due to observed persistence predicted as change. The assessment of the goodness of fit from some spatial overlay is just location based. It cannot provide any information about the morphology of landscape structures, such as connectivity, fractals, and compactness (Li and Yeh, 2004). Predicting correct patch distribution and shapes may, in some cases, be important than developing a model with high accuracy of location (Pijanowski et al., 2006). In this paper, landscape pattern metrics, including Patch Density (PD), Landscape Shape Index (LSI), Perimeter–Area Fractal Dimension (PAFRAC), Shannon’s Diversity Index (SHDI), and Aggregation Index (AI) were also used for the assessment of model performance. All landscape metrics were calculated using landscape ecology program FRAGSTATS and compared to the real change metrics as a percent difference form real change. The comparison was carried out by: 100ðLMrc LMm Þ=LMrc

ð11Þ

Table 3 Confusion matrix between actual and simulated land uses in 2005 simulated by using RBFN-CA models (in the number of cells). Simulated

Actual

Accuracy (%)

Land use

Forest

Orchard

Farmland

Built-up areas

Unused areas

Water

Beach

Forest Orchard Farmland Built-up areas Unused areas Water Beach

43,465 2162 218 756 554 34 354

2266 30,442 1029 6788 3560 77 1254

151 272 1199 619 79 5 44

1650 5731 1929 40,792 12,738 330 3688

1488 4216 854 1054 8607 170 1981

87 249 14 48 86 1186 1079

107 686 43 153 286 258 6190

88.32 69.57 22.68 81.24 33.22 57.57 42.43

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where LM is one of the landscape metrics, m represents the LM for a model simulation and rc is the LM for real change grid.

4. Results Fig. 7 is a geographical representation of the cells by rules of change in the period 2000–2005 (observed, RBFN-CA simulated, BPN-CA simulated). During 2000–2005, the actual land use changes were mainly forest to orchard, unused areas to built-up areas, orchard to built-up areas, orchard to unused areas and forest to built-up areas. Forest to orchard, orchard to built-up areas, orchard to unused areas, forest to built-up areas, and built-up areas to unused areas were the major changes between land use in 2000 and RBFN-CA simulated land use in 2005.Fig. 7(C) shows that land use changes (i.e. forest to orchard, orchard to built-up areas, orchard to unused areas, forest to built-up areas and built-up areas to unused areas) were significant. Comparing the actual land use map and the output map that the model produces, a confusion matrix can be obtained (Tables 3 and 4). For BPN-CA model, the range of accuracy was 20.94–75.98%, while for RBFN-CA the range was 22.68–88.32%. The overall accuracy was 69.04% and 58.04% for RBFN-CA and BPN-CA, respectively. Almost all accuracies for RBFN-CA model exceeded those for BPN-CA, except the simulation of farmland. In addition, for both RBFN-CA and BPN-CA models, the accuracies of land use types (e.g. forest, orchard, and built up areas) were greater than those of others. The reason may be that the proportions of these land use types are higher than those of farmland, unused areas, water, and beach.

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Fig. 8 summarizes the figure of merit for land use categories simulated by RBFN-CA and BPN-CA model. Note that for all land use types, figure of merit for RBFN-CA were greater than those for BPN-CA. For land use types (e.g. forest and orchard) simulated by RBFN-CA and forest simulated by BPN-CA, figure of merit was greater than 50%. That means the amount of correctly predicted change was larger than the sum of the various types of error. For RBFN-CA, there was at least a 55% agreement in the location of all

Fig. 9. Landscape metrics (i.e. patch density, landscape shape index, perimeter–area fractal dimension, Shannon’s diversity Index, and aggregation index) for RBFN-CA and BPN-CA model expressed as a percentage difference from the real change.

Table 4 Confusion matrix between actual and simulated land uses in 2005 simulated by using BPNN-CA models (in the number of cells). Simulated

Actual

Accuracy (%)

Land use

Forest

Orchard

Farmland

Built-up areas

Unused areas

Water

Beach

Forest Orchard Farmland Built-up areas Unused areas Water Beach

38,262 4886 166 1134 524 20 2551

14,355 20,729 728 5162 2132 58 2252

124 418 893 767 69 0 98

2974 6935 1146 40,698 11,034 230 3841

2077 4635 513 5311 3685 63 2086

108 366 9 115 38 753 1360

306 668 28 378 119 370 5854

Fig. 8. Figure of merit for land use types simulated by RBFN-CA and BPN-CA model.

65.74 53.65 25.64 75.98 20.94 50.40 32.44

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cells that were predicted to change, while the overall predictive accuracy for BPN-CA measured by the figure of merit was only 31%. An analysis of landscape metrics for RBFN-CA and BPN-CA are given in Fig. 9. Note that PD, LSI, PAFRAC, and AI did not differ greatly from the real change for RBFN-CA simulation; the largest percent difference (Shannon’s Diversity Index SHDI) from the real change slightly exceeded 4.5%. The BPN-CA model produced as many as 19% more patches than the real change. The LSI and SHDI were significantly higher than observed, 14% and 8%, respectively. Both RBFN-CA and BPN-CA produced greater AI than observed. The AI metric varies considerably across BPN-CA simulations and the real change.

5. Discussion and conclusions In this paper, we parameterized the drivers of land use changes using analysis tools within a geographic information system. Then, these drivers were incorporated into neural networks. Two different learning algorithms (i.e. BPN and RBFN) were applied to determine the explicit transition rules for multiple land use changes. We relied on two historical land use images of the study area to calibrate our models. Goodness-of-fit of the models were compared using a variety of methods including confusion matrix, figure of merit, and landscape metrics. Both the location and landscape metrics based assessments for model simulation showed that the RBFN-CA model performed better than the BPN-CA. The overall accuracy for RBFN-CA and BPN-CA calculated by the confusion matrix was 69.04% and 58.04%, respectively. The RBFN-CA model performed a relatively high predictive ability than the BPN-CA model with the overall accuracy 55.34% (RBFN-CA) vs. 31.25% (BPN-CA) calculated by the figure of merit. Landscape metrics including PD, LSI, PAFRAC, and AI did not differ greatly from the real change for the RBFN-CA simulation. Overall, in this research we demonstrated the usefulness of the RBFN-CA model for simulating multiple classes of land use/cover changes and for projecting future patterns of land use/cover changes. Moreover, bundling of strengths of multiple techniques, such as GIS, CA, and ANNs, helps us to understand the process of land use/cover changes. This combined model mainly has two advantages. First, it can simulate multiple classes of land use/cover changes with spatially explicit models. Second, the neural network module (i.e. RBFNs) of the model can recognize spatial land use/ cover patterns. Compared with other traditional methods, it can avoid many variable choosing and weight determining processes. Although, it is extremely difficult to calibrate CA models, RBFNs are demonstrated as a robust and convenient tool in calibrating simulation models by using Gaussian radial basis functions as its activation function. However, there are several limitations for this combined model. First, the incorporation of human and environment feedbacks in this RBFN-CA model are not fully developed and need further efforts. These feedbacks are related to the use of models as policy support tools and the communication of results of land use/cover change modeling to land use decision makers and other stakeholders. Second, the input spatial variables that we achieved from images or maps might be so limited that no sufficient information is available for land use modeling because land use/cover changes have elements of unpredictability (e.g. emergent and stochastic) and aspects that are non-spatial. Finally, land use systems are complex adaptive systems, and they are characterized by emergence, nonlinearity, feedbacks, self organization, path dependence, adaptation, and multiple scales characteristics. The model presented here is meant only as an example to examine land use changes and could be improved.

Acknowledgement This research is financially supported by National Natural Science Foundation of China (40635028 and 40771001).

References Alonso, W., 1964. Location and Land Use. Harvard University Press, Cambridge, p. 24. Arce-Medina, E., Paz-Paredes, J.I., 2009. Artificial neural network modeling techniques applied to the hydrodesulfurization process. Mathematical and Computer Modeling 49, 207–214. Batty, M., Couclelis, H., Eichen, M., 1997. Urban systems as cellular automata. Environment and Planning B 24, 159–164. Batty, M., Xie, Y.C., 1994. From cells to cities. Environment and Planning B 21, 531–548. Broomhead, D.S., Lowe, D., 1988. Multivariable functional interpolation and adaptive networks. Complex Systems 2, 321–355. Brown, D.G., Page, S.E., Riolo, R., Zellner, M., Rand, W., 2005. Path dependence and the validation of agent-based spatial models of land use. International Journal of Geographic Information Science 19, 153–174. Clarke, K.C., Gaydos, L.Y., 1998. Loose-coupling a cellular automaton model and GIS: long-term urban growth prediction for San Francisco and Washington/Baltimore. International Journal of Geographic Information Science 12, 699–914. Dai, E.F., Wu, S.H., Shi, W.Z., Cheung, C.K., Shaker, A., 2005. Modeling change-patternvalue dynamics on land use: an integrated GIS and artificial neural networks. Environmental Assessment 36, 576–591. de Koning, G.H., Verburg, P.H., Veldkmap, T.A., Fresco, L.O., 1999. Multi-scale modeling of land use change dynamics in Ecuador. Agricultural System 61, 77–93. Fajita, M., 1982. Spatial patterns of residential development. Journal of Urban Economics 12, 22–52. Foley, A.J., DeFries, R., Asner, G.P., Barford, C., Bonan, G., Carpenter, S.R., Chapin, F.S., Coe, M.T., Daily, G.C., Gibbs, H.K., Helkowski, J.H., Holloway, T., Howard, E.A., Kucharik, Ch.J., Monfreda, Ch., Patz, J.A., Prentice, I.C., Ramankutty, N., Snyder, P.K., 2005. Global consequences of land use. Science 309, 570–574. Global Land Project, 2005. Science Plan and Implementation Strategy. International Geosphere–Biosphere Programmer Report No. 53/. International Human Dimensions Programmer Report No. 19. International Human Dimensions Programmer Secretariat, Stockholm, p. 64. Hassoun, M.H., 1995. Fundamentals of Artificial Neural Networks. MIT Press, Cambridge, MA, p. 37. Kumar, K.V., Ravi, V., Carr, M., Kiran, N.R., 2008. Software development cost estimation using wavelet neural networks. The Journal of Systems and Software 81, 1853–1867. Lewis, H.G., Brown, M., 2001. A generalized confusion matrix for assessing area estimates from remotely sensed data. Remote Sensing 22, 3223–3235. Li, W., Hori, Y., 2006. An algorithm for extracting fuzzy rules based on RBF neural network. Transactions on Industrial Electronics 53, 1269–1276. Li, X., Yeh, A.G.O., 2002. Neural-network-based cellular automata for simulating multiple land use changes using GIS. International Journal of Geographic Information Science 16, 323–343. Li, X., Yeh, A.G.O., 2004. Data mining of cellular automata’s transition rules. International Journal of Geographic Information Science 18, 724–744. Liu, J.G., Dietz, Th., Carpenter, S.R., Alberti, M., Folke, C., Moran, E., Pell, A.N., Deadman, P., Kratz, T., Lubchenco, J., Ostrom, E., Ouyang, Zh.Y., Provencher, W., Redman, Ch.L., Schneider, S.H., Taylor, W.W., 2007. Complexity of coupled human and natural systems. Science 317, 1513–1516. Manson, S.M., 2005. Land use in the southern Yucata´n peninsular region of Mexico: Scenarios of population and institutional change. Computers, Environment and Urban Systems 30, 230–253. Moody, J., Darken, C.h., 1989. Fast learning in networks of locally-tuned processing units. Neural Computation 1, 281–294. ¨ Pijanowski, B.C., Alexandridis, K.T., Muller, D., 2006. Modeling urbanization patterns in two diverse regions of the word. Journal of Land Use Science 19, 197–215. Pijanowski, B.C., Brown, D.G., Shellito, B.A., Manik, G.A., 2002. Using neural networks and GIS to forecast land use changes: a land transformation model. Computers, Environment and Urban Systems 26, 553–575. Pijanowski, B.C., Pithadia, S., Shellito, B.A., Alexandridis, K., 2005. Calibrating a neural network-based urban change model for two metropolitan areas of the Upper Midwest of the United States. International Journal of Geographic Information Science 19, 197–215. Pontius, R.G., Boersma, W., Castella, J.Ch., Clarke, K., de Nijs, T., Dietzel, Ch., Duan, Z.Q., Fotsing, E., Goldstein, N., Kok, K., Koomen, E., Lippitt, Ch.D., McConnell, W., Pijanowski, B., Pithadia, S., Sood, A.M., Sweeney, S., Trung, T.N., Veldkamp, A.T., Verburg, P.H., 2008. Comparing the input, output, and validation maps for several models of land change. Annals of Regional Science 42, 11–37. Pontius, R.G., Gilmore, R., Lippitt, C.D., Hall, C., 2001. Modeling the spatial pattern of land-use change with GEOMOD2: application and validation for Costa Rica. Agriculture, Ecosystems and Environment 85, 191–203. Pontius, R.G., Gilmore, R., Malanson, J., 2005. Comparison of structure and accuracy of two land change models. International Journal of Geographical Information Science 19, 243–265.

Y. Wang, S. Li / Computers & Geosciences 37 (2011) 111–121

Powell, M.J., 1987. Radial basis functions for multivariable interpolation: a review. In: Mason, J., Cox, M. (Eds.), Algorithms for Approximation. Clarendon Press, Oxford, pp. 143–167. Ros, F., Pintore, M., Deman, A., Jacques, R.C., 2007. Automatical initialization of RBF neural networks. Chemometrics and Intelligent Laboratory Systems 87, 26–32. Silva, E.A., Clarke, K.C., 2002. Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal. Computers, Environment and Urban Systems 26, 525–552. Sui, D.Z., Zeng, H., 2001. Modeling the dynamics of landscape structure in Asia’s emerging Desakota regions: a case study in Shenzhen. Landscape and Urban Planning 53, 37–52. Tettamanzi, A., Tomassini, M., 2001. Soft Computing: Integrating Evolutionary, Neural, and Fuzzy Systems. Springer-Verlag, Berlin, p. 327. Tobler, W.R., 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography 46, 234–240. Torrens, P.M., 2009. Cellular automata. In: Kitchin, R., Thrift, N. (Eds.), International Encyclopedia of Human Geography. Elsevier, London, pp. 1–4.

121

Torrens, P.M., Benenson, I., 2005. Geographic automata systems. International Journal of Geographic Information Science 19, 385–412. Turner II, B.L., Lambin, E.F., Reenberg, A., 2007. The emergence of land change science for global environmental change and sustainability. Proceedings of the National Academy of Sciences of the United States of America 104, 20666–20671. Verburg, P.H., Soepboer, W., Veldkamp, T.A., Limpiada, R., Espaldon, V., Mastura, S.A., 2002. Modeling the spatial dynamics of regional land use: the CLUE-S model. Environmental Management 30, 391–405. Verburg, P.H., Veldkamp, T.A., 2005. Spatial modeling to explore land use dynamics. International Journal of Geographic Information Science 19, 99–102. Vliet, V.J., White, R., Dragicevic, S., 2009. Modeling urban growth using a variable grid cellular automaton. Computers, Environment and Urban Systems 33, 35–43. White, R., Engelen, G., 2000. High-resolution integrated modelling of the spatial dynamics of urban and regional systems. Computers, Environment and Urban Systems 24, 383–400.