*2.6. Accuracy Assessment*

Classification accuracy was assessed based on the classification accuracy statistics, the error matrix (user/producer's accuracy and omission/commission error), overall accuracy and kappa statistic [76]. Validation of the classification maps produced from the support vector machine implementation was performed against the set of validation pixels for each class collected following the procedure [77]. In addition to the classification statistics, the land cover classification was generated from the support vector machine algorithm and shows correspondence between the classification result and a reference data. The value of reference data was collected in 1458 pixels from the field in Equations (2)–(5).

$$\text{Kappa} = \frac{N\sum\_{i=1}^{r} \text{Xii} - \sum\_{i=1}^{r} \text{Xi} + (\text{X} + i)}{N^2 - \sum\_{i=1}^{r} \text{Xi} + (\text{X} + i)} \times 100\% \tag{2}$$

$$\text{Overall Accuracy} = \frac{\sum\_{i=1}^{r} Xii}{N} \times 100\% \tag{3}$$

$$\text{User's Accuracy} = \frac{\text{Xii}}{X+i} \times 100\% \tag{4}$$

$$\text{Producer's Accuracy} = \frac{\text{Xii}}{X+i} \times 100\% \tag{5}$$

where *N* is the number of all pixels used for observation, *r* is the number of rows in the error matrix (number of classes), *Xii* is diagonal values of the contingency matrix of row *i* and column *i*, *X* + *i* is column pixel number *i*, and *Xi* + row pixel number *i*.

### *2.7. Markov Chain*

Modeling using Markov-Cellular Automata has been widely applied in several fields by researchers, including for the study of regional-scale land-use change, watershed managemen<sup>t</sup> [78,79], regional monitoring cities [80–83], monitoring of plantation and agricultural areas [84], monitoring of erosion [85], simulating forest cover change [86], evaluating the integration of land use and climate change [87], and monitoring sand areas [88]. In 2015, Halmy et al. (2015) [88] used the Markov-Cellular Automata model to predict sand areas using Landsat TM 5 data, which yields 90% accuracy. The results show that the Markov-Cellular Automata model is a useful model for applying and predicting land cover.

Markov Chain determines how much land cover would be estimated to change from the latest date to the predicted date [89]. In this study, the Cellular Automata (CA) -Markov model was applied to predict the 2028 LULC in the Sembilang National Park area to identify variations in future mangrove land use. First, classified images from the period of 1989 and 1998; between 1998 to 2002, and 2002 until 2015 were selected as input into the model, to calculate matrix of conversion areas and conversion probabilities. The transition probability maps were used to produce maps of land use for the year of 2028. In an iterative process CA-Markov uses the transition probability maps of each land cover to establish the inherent suitability of each pixel to change from one land use type to another. The transition area matrix shows the total area (in cells) expected to change in the next period of 1989–1998, 1998–2002, and 2002–2015.

The prediction of land use changes is calculated by the following Equation (6) [89,90]:

$$S(t, \ t+1) = \text{Pi}j \times S(t) \tag{6}$$

where *S* (*t*) is the system status at time of *t*, *S* (*t* + 1) is the system status at time of *t* + 1; *Pij* is the transition probability matrix in a state [90]. If *P* is transition probability, namely the probability of converting current state to another state in next period [91], the expression is as follows:

$$P\_{ij} = \begin{bmatrix} P\_{11} & P\_{12} & \dots & P\_{1n} \\ P\_{21} & P\_{22} & \dots & P\_{2n} \\ \dots & \dots & \dots & \dots \\ P\_{n1} & P\_{n2} & P\_{nn} \end{bmatrix} \tag{7}$$

$$\left(0 \le P\_{ij} \le 1\right) \tag{8}$$

where *P* is the transition probability; *Pij* stands for the probability of converting from current state *i* to another state *j* in next time; *Pn* is the state probability of any time. Low transition will have a probability near 0 and high transition have probabilities near 1 [44].

#### *2.8. Cellular Automata (CA)*

The Cellular Automata (CA) is produces to determine iteration times, combining transition area matrix and potential transition maps as the CA local transition rule, land use map in the future could be simulated. In this study, Markov Chain results from data in the form of a transition probability matrix, transition area matrix, and a set of conditional probability images (1989–1998, 1998–2002) and

actual land use maps in 2002 and 2015 were applied with the Cellular Automata model to obtain predictions of land cover in 2002 and 2015.

The CA model can be expressed as follows in Equation (9) [90]:

$$S(t, \ t+1) = f\left(S(t), \ N\right) \tag{9}$$

where *S* is the set of limited and discrete cellular states, N is the Cellular field, *t* and *t* + 1 indicate the di fferent times, and *f* is the transformation rule of cellular states in local space.
