The term “Artificial Neural Network (ANN)” has been inspired by human biological nervous system [

25]. In a typical ANN model, simple nodes are connected together to form a network of nodes. Some of these nodes are called input nodes; some are output nodes and in between there are hidden nodes [

26]. Multi Layer Perceptron (MLP) is a feed-forward Neural Network with one or more layers between input and output layers. The great advantage of using MLP perceptron neural network is that it gives the opportunity to model several or even all the transitions at once [

12].

#### 3.4.1. The Feed-Forward Concept of Multi Layer Perceptron Neural Network

MLP neural network uses the back propagation (BP) algorithm. The calculation is based on information from training sites [

12]. Back propagation involves two major steps, forward and backward propagation. The input that a single node receives is weighted as:

(14)

where, w_{ij} = the weights between node i and node j; O_{i} = the output from the node i

The output from a given node j is computed as [

26]:

(15)

f = a non-linear sigmoid function that is applied to the weighted sum of inputs before the signal passes to the next layer

This is known as “Forward Propagation”. Once it is finished, the activities of the output nodes are compared with their expected activities. In normal circumstances, the network output differs from the desired output (a set of training data, e.g., known classes). The difference is termed as the error in the network [

26]. The error is then back-propagated through the network. Now the weights of the connections are corrected as follows [

12]:

(16)

η = the learning rate parameter; δ_{j} = an index of the rate of change of the error; α = the momentum parameter.

The process of the forward and backward propagation is repeated iteratively, until the errors of the network minimized or reaches an acceptable magnitude [

26]. The purpose of training the network is to get proper weights both for the connection between the input and hidden layer, and between the hidden and the output layer for the classification of unknown pixels [

12]. Several factors affect the capabilities of the neural network to generalize [

26]. These include:

#### 3.4.3. Number of Training Samples and Iterations

The number of training sample also affects the training accuracy. Too few samples may not represent the pattern of each category while too many samples may cause overlap. Again too many iterations can cause over training that may cause poor generalization of the network [

12]. Over training can be prevented by early stopping of training [

25]. The acceptable error rate is evaluated based on the Root Mean Square (RMS) Error [

25]:

(18)

where, N = the number of elements; i = the index for elements; e_{i} = the error of the ith element; t_{i} = the target value (measured) for i^{th} element; a_{i} = the calculated value for the i^{th} element.

#### 3.4.4. Multi Layer Perceptron Markov Modeling

The basic concept of modeling with MLP neural network adopted in this research is to consider the change in built-up area over the years. In general, it means other land cover types are primarily contributing to increase the built-up area. At this stage, the issue of which variables affect the change to built-up area (1989–1999) has been considered. Therefore, only the transitions from “water body to built-up area”, “vegetation to built-up area”, “low land to built-up area” and “fallow land to built-up area” have been considered for model simulation. These four transitions have been termed as “All” here.

Figure 10 exhibits the transition from all to built-up area.

**Figure 10.**
Transition from all to built-up area (1989–1999).

**Figure 10.**
Transition from all to built-up area (1989–1999).

It is logical that new areas will be converted to built-up area where there are existing built-up areas. Therefore six driver variables have been selected for MLP_Markov modeling. These are (1989–1999): Distance from all to built-up area, distance from water body, distance from vegetation, distance from low land, distance from fallow land and empirical likelihood image).

The empirical likelihood transformation is an effective means of incorporating categorical variables into the analysis (

Figure 11). It has been produced by determining the relative frequency of different land cover types occurred within areas of transition (1989 to 1999). The numbers (legend) indicate the likelihood of changing into built-up area. The higher the value the likeliness of the pixel to change into the built-up cover type is more.

Now it is important to test the potential explanatory power of each variable. The quantitative measures of the variables have been tested through Cramer’s V [

27]. It is suggested that the variables that have a Cramer’s V of about 0.15 or higher are useful while those with values of 0.4 or higher are good [

12].

After getting satisfactory Cramer’s V values for all the driving variables, now the turn is to run MLP neural network model. For this purpose, 10,000 iterations have been chosen. The minimum number of cells that transitioned from 1989 to 1999 is 4,794. Therefore, the maximum sample size has been chosen as 4,794. For each principal transition particular weights have to be obtained. The RMS error curve has been found smooth and descent after running MLP neural network. After all these combinations, the MLP running statistics gives a very high accuracy rate of 91.36% (this accuracy is a measure of calibration, not validation). Based on these running statistics the transition potential maps have been produced (

Figure 12). These maps depict, for each location, the potential it has for each of the modeled transitions [

12]. These are not the probability maps where the sum of values for a particular pixel location will not be 1. The reason behind this is because the MLP neural network outputs are obtained by applying fuzzy set to the signals into values from 0 to 1 with activation function (sigmoid). Here the higher values represent a higher degree of membership for that corresponding land cover type [

12].

**Figure 11.**
Empirical likelihood image of changing into built-up areas (1989–1999).

**Figure 11.**
Empirical likelihood image of changing into built-up areas (1989–1999).

**Figure 12.**
Transition potential maps from all to built-up area (1989 to 1999).

**Figure 12.**
Transition potential maps from all to built-up area (1989 to 1999).

#### 3.4.5. Future Prediction Using Multi Layer Perceptron Markov Model

Using this kind of MLP neural network analysis it is possible to determine the weights of the transitions that will be included in the matrix of probabilities of Markov Chain for future prediction. The transition probabilities are shown in

Table 10. Based on all these information from MLP neural network, the final land cover map of 2009 (

Figure 13) has been simulated through Markov chain analysis. The whole procedure, for predicting the land cover map by this way, has been termed as “MLP_Markov” model.

**Figure 13.**
MLP_Markov projected land cover map of Dhaka City (2009).

**Figure 13.**
MLP_Markov projected land cover map of Dhaka City (2009).

**Table 10.**
Transition probabilities grid for Markov chain (1989 to 1999) in MLP modeling.

**Table 10.**
Transition probabilities grid for Markov chain (1989 to 1999) in MLP modeling.
| Built-up Area | Water Body | Vegetation | Low Land | Fallow Land |
---|

**Built-up Area** | 0.7823 | 0.0174 | 0.0347 | 0.0194 | 0.1463 |

**Water Body** | 0.2079 | 0.1264 | 0.1008 | 0.1927 | 0.3721 |

**Vegetation** | 0.1529 | 0.0779 | 0.3887 | 0.1071 | 0.2734 |

**Low Land** | 0.0695 | 0.3634 | 0.0467 | 0.4054 | 0.1150 |

**Fallow Land** | 0.3825 | 0.0133 | 0.2413 | 0.0185 | 0.3445 |