Land Use Changes Modeling Based on Different Approaches: Fuzzy Cognitive Maps, Cellular Automata and Neural Networks MARIA MOISE Computer Science for Business Management Faculty Romanian American University 1 B, Expoziţiei Avenue, Sector 1, 012101 Code, Bucharest ROMANIA maria.moise@rau.ro http://www.rau.ro Abstract: For modeling land use changes there are different approaches based on: Fuzzy Cognitive Maps, Cellular Automata, Neural Network, Agent Based Models etc. Fuzzy Cognitive Maps (FCMs) approach is a modelling methodology, developed as an expansion of cognitive maps. FCMs belong to the class of neuro fuzzy systems and they are able to incorporate human knowledge and adapt it through learning procedures. FCMs can be used for modeling land use changes because they are capable of modeling scenarios described in terms of significant events or concepts and their causeeffect relationships. Cellular Automata models consist on a simulation environment represented by a grid of space (raster cells), in which the state of a cell is changing to another state by using a set of transition rules taking into account the attributes of cells in its vicinities. Although CA models are widely applied to simulate various spatio-temporal phenomena, particularly for modeling land use changes. However, the implementing of a CA model and its calibration is complicated because there is a large set of parameters of the transition rules and also the numerical values of these parameters that must be found. For Cellular Automata calibration there are statistical techniques (logistic and multiple regressions, principal component analysis and multivariate analysis of variance) and computational intelligence techniques (Artificial Neural Network, genetic algorithm and data mining). By ANN training can be obtained the parameter values needed for simulating land use changes. This paper is a result of a research made in the Future Policy Modeling FUPOL project, financed by FP7 (www.fupol.eu). Key-Words: policy domains, land use changes, Fuzzy Cognitive Maps, Cellular Automata, Neural Network 1 Introduction The strategies of European urban planning take into account more than 20 policy domains such as: Urban Planning, Land Use, Environment, Economy, Housing, Community Facilities, Transport and Movement, Urban Segregation, Migration, Demography, Social Affairs, City Treasury, Tourism etc. These policy domains will be modeled into FUPOL project (www.fupol.eu), based on new approach of traditional politics, in order to develop advanced ICT tools to support policy design and implementation. Land use is the human use of land, and it involves the management and modification of natural environment or wilderness into built environment such as fields, pastures, and settlements. It has also been defined as "the arrangements, activities and inputs people undertake in a certain land cover type to produce, change or maintain it [3]. Related with the policy domain Land Use there are some key questions [3]: - Where is the industry likely to settle down? - How much of the agricultural land do we need to convert to support economic growth? - How much of the green space do we need to convert to support economic growth? - How much of the green space do we need to convert to support expected economic growth or shrinkage? ISBN: 978-1-61804-099-2 254
- The population is growing; what is the most likely land use pattern in 20 years, where do we expect people do build new houses, industry and offices? - Do we have excessive urban sprawl? The answer to these questions helps urban decision makers and governments to manage the development of land within their jurisdictions and to make a systematic assessment of land and water potential, alternatives for land use, and economic and social conditions in order to select and adopt the best land-use options. Land use changes are complex spatial processes resulting from the interactions of socioeconomic (for example, population growth), biophysical (for example, slope and soil quality), and geographic (for example, proximity and accessibility to services) factors operating at different spatial and temporal scales [10], [14]. Historical land use patterns together with current trends in a region can be used to model future land use. In a region can be distinguished different land use types such as: agriculture, forest, water, urban, etc. In time, land use changes are passing from one type to another. In fig. 1 are presented the relationships between land use changes. Land Use 1 Land Use 2 Land Use 3 Land Use 4 Land Use n Fig.1 The relationships between land use changes Land Use 1 Land Use 2 Land Use 3 Land Use 4 Land Use n Fig. 1 The relationships between land use changes For modeling land use changes, many computer-based models were developed. Modelling land use change started in the 1950s, between 1970s and 1980s there was a demonstrated less activity. After 1990s, as a result of the improvement in spatial data availability and advancements in computer technologies and geographic information systems (GIS) this activity has been revived intensely [15]. For modeling land use changes there are different models, such as: regression-type models, spatial transition-based models, Fuzzy Cognitive Models, Agent Based Models etc. The regression-type models of land use change are useful in exploring the various social, economic and spatial variables that drive change and are useful in evaluating the impacts of alternative policies on land use and development patterns. The relative contribution of different variables for predicting land use change can be easily attained under the regression-type model. The spatial transition models are an extension of a spatial Markov technique and a form of stochastic cellular automata. Cellular Automata (CA) models consist of a simulation environment represented by a raster image (gridded space), in which a set of transition rules determine the attribute of each given cell taking into account the attributes of cells in its neighbourhood. These models have problems in defining simulation parameter values and the Artificial Neural Network can be used to automatically determine these parameters. The Artificial Neural Networks (ANN) have the capacity to recognize and classify patterns through training or learning processes and can be used to obtain the CA parameter values needed for simulating land use changes. 2 Fuzzy Cognitive Maps for land use modeling Cognitive maps (CMs) and are wellestablished techniques that attempt to emulate the cognitive process of human experts on specific domains by creating causal models as signed/weighted directed graphs of concepts and the various causal relationships that exist between those concepts [1], [8]. 2.1 FCM Modeling methodology FCM Modeling methodology for land use consists on: a Description of Fuzzy Cognitive Maps (FCM) b Selection of Factors and Causal Relations ISBN: 978-1-61804-099-2 255
c Coding the cognitive maps into adjacency matrices d Designing the FCM e Simulating scenarios 2.1.1 Description of Fuzzy Cognitive Maps For the definition of FCMs is needed to provide: a Nodes (concepts Ci, i = 1,..., N, where N is the total number of concepts). Each node it is characterized by a value, Ai [0, 1], i = 1,..., N. The nodes are interconnected through weighted arcs, which significance the relations among them; b Edges/arcs (causal links among the concepts); c Weights (represent how much one node influences another). The weight W ij is analogous to the strength of the causal link between two concepts C i and C j. The positive sign of W ij indicates a direct relation between the two concepts that means a positive causality, the negative sign of W ij indicates an indirect relation between the two concepts that expresses negative causality, and W i =0 expresses no relation. Human knowledge and experience on the system determines the type and number of nodes, as well as the initial weights of the FCM; d Activation events at different moment t. 2.1.2 Selection of Factors and Causal Relations Cognitive maps can be obtained in four ways: - from questionnaires - by extraction from written texts - by drawing them from data that shows causal relationships - Through interviews with people who draw them directly. Examples of questions related to a land-use FCM [4]: What are the characteristics that make this area unique / special? What are the most important things in your area? This area has changed in the last years, how did that affect the uniqueness of the area and what were the causes of change? What does the informant perceive as important concepts in this area, and how is this being influenced by other concepts? What does the informant perceive as important concepts in this area, and how is this being influenced by other concepts? When you experience this place: - What is important for you? - What do you appreciate? - What do you not like? What: - Affects X - Causes X to have the value you describe? Which factors (natural changes, human activities etc.) can change this system? What - Do you believe can change this picture? - Have changed since you started coming here? (natural changes / changes caused by humans) What if: - More people are coming? - More noisy people are coming? - There are decided limitations to the management? - There are decided limitations to the traffic? How affects these concepts each other (positively, negatively, feed-back mechanisms)? What happens with X when Y becomes larger/smaller? What happens then with Z? How strong are these effects (small, medium, large)? How large effect positive/negative effect does concept X have on concept Y (small/medium/large)? Important is it for concept X that concept Y changes (small/medium/large)? 2.1.3 Coding the cognitive maps into adjacency matrices The construction of a FCM requires the input of human experience and knowledge on the system under consideration. - Transformation of the linguistic weights into fuzzy sets ISBN: 978-1-61804-099-2 256
After the interviews, the Cognitive Maps are transformed into matrices in the form (W ij )ij [7]. The linguistic variables that describe each arc, for each interviewed are characterized by the fuzzy sets whose membership functions are shown in the fig. 2: local people and other stakeholders could understand what was meant with each scenario and could relate to the outputs that were generated by the FCMs. By using peoples experiences, we make use of trends relevant to the affected group targeted for analysis. 2.2 FCM for Land Use domain The land areas could be divided into the following groups [6] (fig. 3): Fig. 2 Membership functions for fuzzy weights of FCMs The linguistic variables are combined, and the aggregated linguistic variable is transformed to a single linguistic weight, through the SUM technique. Finally, the Center of Area (CoA) defuzzification method [8] is used for the transformation of the linguistic weight to a numerical value within the range [ 1, 1]. 2.1.4 Designing the FCM Other steps must be followed in order to define a proper FCM: - Augmenting individual cognitive maps and then adding them together to form stakeholder social cognitive maps; - Analysing the structure of individual and social cognitive maps using graph theoretical indices (density (clustering coefficient) of a fuzzy cognitive map [5], hierarchy index (h) [11]; - Analysing the differences and similarities in variables among stakeholder groups; - Condensing complex cognitive maps into simpler maps for comparison purposes; - Analysing the outcomes of cognitive maps using neural network computation. 2.1.5 Simulating scenarios In the scenario analyses, FCMs indicate the direction in which the system will move given certain changes in the driving variables and also give an idea of the magnitude of system fluctuations after a disturbance. Using FCMs in the scenario analysis was powerful because Fig. 3 Land use classification In fig. 4 is illustrated the FCM for land use and in Table 1 is illustrated a possible scenario, where the Transport factor was reduced by approximately two thirds (factor 3). Fig. 4 FCM for land use [4] ISBN: 978-1-61804-099-2 257
Table 1 [4] No 1 2 3 4 5 6 7 8 9 10 Factors/Concepts (a) Steady state (b) Scenario #1 (c) Steady state for Scenario #1 (d) Residential 0.73 0.73 0.730188 Commercial 0.6510341 0.6510341 0.6486184 Transport 0.7231338 0.5 0.5 Recreation 0.5444086 0.5444086 0.5478634 Infrastructure 0.6999961 0.6999961 0.6660389 Real estate 0.6891712 0.6891712 0.6876385 Planning 0.6896019 0.6896019 0.6905225 Households 0.738507 0.738507 0.7373247 Housing utilities 0.712200 0.712200 0.7121576 Natural environment 0.526563 0.526563 0.549282 The results regarding analysis of scenario #1 are presented Table 2. Table 2 [4] 3 Cellular Automata (CA) CA are cell-based methods that can model twodimensional space, and because of this underlying feature, and they can be used to simulate land use change, urban development, urban growth, urban planning and other changes of geographical phenomena. CA model uses spatial variables and for each variable it has a weight associated, which shows the contribution to land use change. Before the simulation by using CA model it is necessary to define numerous parameters that have great effects on the results of simulation. Problem with CA models is to define transition rules and model structure. An example of a land-use change is presented in fig. 5, where an hypothetical region is represented as a raster image (grid cells) and the cells can have one of 4 land use states such as: agriculture (yellow colour), urban (red colour), forest (green colour) and water (blue colour). Fig. 5 An example of land use change represented by a raster image Each cell of a raster image has a neighborhood (fig. 6). Neighborhood of a cell consists of the surrounding adjacent cells, including the cell itself. At the time t=0 each cell has a state S 0 and at time t=n the cell state become S n. The transition of a cell from one state to other state is influenced by neighborhood cells and other factors such as: distance to main road, distance to railway etc. The CA model works as follows for example in fig. 5: - for every cell the model reads the state of the cells located within an extended neighborhood composed of thirteen cells; - model selects what would the new state of the cell be at the next time step (for example ten years later), according to the predefined transition rules. a. b. c. d. Fig. 6 Different types of neighborhoods a. Neighborhood for 1-dimensional CAs b. Von Neumann neighborhood, for 2 dimensional CAs c. Moore neighborhood, for 2 dimensional CAs d. Oher type of neighborhood, for 2 dimensional CAs ISBN: 978-1-61804-099-2 258
For a CA model is necessary to define the transition rules, process known as CA calibration that consists on: - finding the parameters of the predefined transition rules; - finding the numerical values of these parameters so that the rules closely correspond to the land-use change processes reflected in the historical data The rules are based on an intuitive understanding of the processes as there is no obvious way of finding which parameter should or should not be included in the model [16]. The CA models can be used with success because their operationally, simplicity and ability to embody logics - as well as mathematics-based transition rules. However, the calibration of CA models is very difficult when there is a large set of parameters. Using cellular automata (CA) for simulation of land use changes is difficult, because there are numerous spatial variables and parameters that must be utilized. In this context, some relevant papers [17], [9], [2], [13] show that most of the parameter values for CA simulation can be automatically determined by the training of an Artificial Neural Network (ANN). Advantages of applying the CA models to land use: - CA are explicitly spatial - Cell state is typically a land use - CA models are often designed to test whatif scenarios and policies - CA is of a limited set of equations and transitions rules - Model input/output are in most cases raster images (used/created in GIS/remote sensing software) - CA can be seen as an extension of GIS, in which dynamics are applied on the data - CA models are good for capturing patterns of land use changes - In a CA model may be included a stochastic factor such as: if the probability of a land use change of a cell is greater than a random value, then the change will occur. 4 Artificial Neural Networks (ANN) The ANN of feedforward type based on backpropagation algorithm can be used for obtaining the CA parameter values needed to simulate land use changes. The feedforward ANN architecture with multiple neurons on output layer (fig. 7) can be used to obtain CA parameter values in order to simulate land use changes. In this architecture there are n neurons in input layer, representing the site attributes (for example distance to main road, distance to railway, distance to city center etc.) and number of neighborhood cells (for example number of urban cells in neighborhood, number of agriculture cells in neighborhood, number of forest cells in neighborhood etc.). Also there are m neurons on hidden layer (that may be equal or less than number of neurons on input layer) and l neurons in output layer. Calculated output of each neuron in output layer represents the transition probabilities for land use changes. The defining of the site attributes and the number of neighborhood cells (neurons) in input layer depends on the studied region. Also, the setting of neurons (desired values) in output layer depends on the land use patterns of the studied region. Fig. 7 ANN architecture [4] The backpropagation algorithm that uses a sigmoid activation function done by (1) was implemented in VB programming language in order to train the ANN. (1) ISBN: 978-1-61804-099-2 259
where, - net j (t) - the signal received by neuron j n the hidden layer at time t (2) - x i (t) - the site attribute (normalised) for neuron i in the input layer - x i (t) = x ij (t), so x i (t)= x ij (t) because for the neurons in input layer in back propagation algorithm there isn t processing - w ij - weight of x ij The transition probability of land use change P c (t) for cell c is done by the formula: P c ( t, k) where, ( t) C, k ( t) C, k in output layer 1 e 1 net ( c, t) k (3) is calculated output of neuron k 5 Conclusions The approach presented in this paper was proposed in FUPOL project as methodology for modeling land use changes. The FCM models are based on people knowledge and Cellular Automata and Artificial Neural Networks are based on spatial data that can be obtained from GIS database. References: [1] Axelrod, R., 1976, Structure of Decision: The Cognitive Maps of Political Elites, Princeton University Press, Princeton, New Jersey. [2] Carpenter, G.A., Gopal, S., Shock, B.M., Woodcock, C.E., 2001. A neural network method for land use change classification, with application to the Nile River Delta. Technical Report CAS/CNS-TR-2001-010, Boston, MA: Boston University. [3] FUPOL Deliverable 2.1, 2012 [4] FUPOL Deliverable 2.2, 2012 [5] Hage, P. and Harary, F., 1983, Structural Models in Anthropology. Oxford University Press, New York. [6] Kajita, Y., Toi, S., Tatsumi, H., Yamauchi, S., 2005, An Approach for Predicting Land Use Changes in an Urbanization Control Area - A Case Study of a Japanese Regional Hub City, Proceedings of European Regional Science association. [7] Khan, M. S. and Quaddus, M., 2004, Group Decision Support Using Fuzzy Cognitive Maps for Causal Reasoning, Group Decision and Negotiation, Vol. 13, Issue: 5, Publisher: Springer, pp. 463-480. [8] Kosko, B., 1986, Fuzzy cognitive maps, International Journal of Man-Machine Studies, Vol. 24, pp. 65-75. [9] Li, X. and Yeh, A. G.-O., 2002, Neuralnetwork-based cellular automata for simulating multiple land use changes using GIS, International Journal of Geographical Information Science, Vol. 16, Issue 4, pp. 323-343. [10] Liu, Y., & Phinn, S. R., 2003, Modelling urban development with cellular automata incorporating fuzzy-set approaches, Computers, Environment and Urban Systems, Vol. 27, Issue 6, pp. 637-658. [11] MacDonald, N., 1983, Trees and Networks in Biological Models, John Wiley and Sons, New York, 215 pp. [12] Moise M., 2010, Artificial Intelligence and Expert Systems IV -th Edition, ProUniversitaria Publishing House, Bucharest, pp. 153-166. [13] Pijanowski, B. C., Brown, D. G., Shellito, B. A. and Manik, G.A., 2002, Using neural networks and GIS to forecast land use changes: a Land Transformation Model, Computers, Environment and Urban Systems, Vol. 26, Issue 6, pp. 553-575. [14] Verburg, P. H., de Nijs, T. C. M., Van Eck, J. R., Visser, H., & de Jong, K., 2004, A method to analyse neighbourhood characteristics of land use patterns, Computers, Environment and Urban Systems, Vol. 28, Issue 6, pp. 667-690. ISBN: 978-1-61804-099-2 260
[15] Wegener, M., 1994, Operational Urban Models: State of the Art, Journal of the American Planning Association, Vol. 60, Issue 1, pp. 17-29. [16] Wu, F., 2002, Calibration of stochastic cellular automata: the application to ruralurban land conversions, International Journal of Geographical Information Science, Vol. 16, Issue 8, pp. 795-818. [17] Xu, X., Zhang, J. and Zhou, X., 2008, Modeling urban land use changes in Lanzhou based on artificial, neural network and cellular automata, Geoinformatics 2008 and Joint Conference on GIS and Built Environment: Geo-Simulation and Virtual GIS Environments. Proceedings of SPIE, Vol. 7143, pp. 71431A-71431A-10. ISBN: 978-1-61804-099-2 261