## 3 Data and Methodology
### Urban LULC Modeling
#### 3.4.2 Multi-Layer Perceptron-Markov Chain (MLP-MC)  
This method uses the combination between multi-layer perceptron (MLP) and MC to predict the future LULC. The MLP-MC performed in Land Change Modeler (LCM) utilizes three stepwise processes: change analysis, transition potential modeling and change prediction [28; 36]. The details of each process are examined in detail. * Change Analysis  
This step comes with two times of LULC maps like change analysis process. It uses these to identify the major transitions that can be modeled separately like sub-model in the next step. * Transition Potential Determination  
The transition potential analysis is also an important part to determine driver factors that cause a conversion between a pair of LULC classes [31; 41; 42]. Some affirmation data were passed through the Euclidean distance function to generate distance maps. Statistical data such as slope, population, and economic data are also used to calculate the density and growth rate maps. All of these factors are shown in Table 2. \begin{table}
\begin{tabular}{l l} \hline \hline
**Data** & **Detailed Description** \\ \hline Distance to agriculture & Distance to any agricultural activity \\ Distance to BTS and MRT & Distance to BTS and MRT line \\ Distance to built-up area & Distance to any man-made construction \\ Distance to forest & Distance to any forest \\ Distance to main road & Distance to any permanent road \\ Distance to miscellaneous & Distance to any open land and grassland \\ Distance to river & Distance to permanent flowing water and surface sources \\ Distance to urban center & Distance to city center \\ Growth rate of economics & Growth rate of GPP \\ Growth rate of housing & Annual growth rate of housing \\ Growth rate of population & Annual growth rate of population \\ Housing density & Housing unit density per square kilometer \\ Population density & Persons per square kilometer \\ Slope & Mean slope in degrees \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Definition of driving factors of LULC conversion in each specific time. In the driving factors identification, Cramer's \(V\), a popular nominal scale measurement, based on qui-square, was applied to identify the most associated factors between two categorical maps. Equation (1) shows the formula of [PERSON]'s \(V\) statistic where \(\varphi\) (phi) is the coefficient of contingency and t is the smaller of the number of rows minus one or the number of columns minus one [41]. \[V=\sqrt{\frac{\varphi^{2}}{\text{t}}} \tag{1}\]  
According to the literature, if the Cramer's \(V\) value is about 0.15 or higher, it means that the association is useful. Moreover, if its value is greater than 0.4, the association is good [38]. Once all the explanatory factors were tested in each land transition, the LCM adopted MLP to generate the transition potential maps. The MLP is a feed-forward artificial neural network in which all data are passed from input layers to output layers. Each neuron calculates a combined value that is the result of the multiplication of values in the nodes of the previous layer by the connection weights between the nodes. This combined value is then the input to an activation function of the node, typically a non-linear activation function such as a sigmoid function [43; 44]. Further, a back propagation training algorithm is typically used for the supervised training of the neural network. The algorithm iteratively changes the weights of the neural connections between the nodes of the different layers in such a manner that the error between the nodes' outputs and their desired outputs is minimized [45]. In each land transition sub-model of this study, the MLP generates a random set of sample cells that have and have not experienced the transition. Therefore, each sub-model, consisting of one transition and two examples of classes, including one transition class and one persistence class, was fed.