## 3 Proposed Methodology
### Decision Tree Algorithm  
The decision tree classification has advantages in terms of flexibility, nonparametric nature and capable to handle non-linear relations between features and classes. An input sample can be classified into its possible classes through tree structures of decision tree formation [14; 33]. The tree structures formation defined in decision rules model within based on if/else instruction. The decision tree is one of the well-known classification tools since it gives prudent accuracy and low cost computation [11]. In this paper, the decision tree application i.e., a type of supervised learning, is simulated in MATLAB using 'fittree' command. The targeting output will supervise the training sets using recursive binary partitioning method. Succeeding questions with yes or no results are inquired for separating the sample space. The nodes are the spots where the test is performed on the elements. The test results then are represented to another node that could be seen as branches. There are three kinds of node presenting in decision tree namely the root node, the leaf node, and the internal node, as illustrated in Figure 11. The outcome of the test is determined by the purity of each node. The node will stop one it achieves an optimal post level of class purity. The optimal level is defined when the node is having the only output types in the node. An element value will be tested against the decision tree whenever to classify the new samples. Class prediction for the tested samples is maintained by the attribution path from the root node to a leaf node. The basic process of getting a decision tree is to repetitively find the attribute to be tested on a node and then subsidiary to another node. This whole attribution process to identify test and branch is known as splitting.  
The splitting process has a role to minimize the impurity in the dataset which corresponding to class at the later stage. The process requires information gain calculation which must be accomplished into two stages which are entropy and entropy splitting index.  
Figure 11: Decision tree attributes (**a**) and division process (**b**).  
Based on the Figure 11b\(t_{P}\) is parent node, \(t_{L}\) is left child node, and \(t_{R}\)--right child node. The entropy index also known as impurity and the measure of impurity/entropy \(i(t)\) at node t is denoted as;  
\[i(t)=-\sum_{j=1}^{k}p\big{(}w_{j}|t\big{)}\log\ p\big{(}w_{j}|t\big{)} \tag{29}\]  
where \(p\big{(}w_{j}|t\big{)}\) is the proportion of the pattern \(x_{j}\) allocated to class \(w_{j}\) at node \(t\). Each non-terminal node is divided into node \(t_{L}\) and \(t_{R}\) as shown where \(x_{j}^{R}\) represented the best splitting values of variable \(x_{j}\). Corresponding proportions of entities new node are \(P_{L}\) and \(P_{R}\). The best division (entropy splitting index) is that which maximized the difference is given by Equation (30).  
\[\Delta i(t)=i(t_{P})-P_{R}i(t_{L})-P_{L}i(t_{R}) \tag{30}\]  
Furthermore, to find the best split predictor at each node, this study implemented selection predictor algorithm namely all splits, curvature, and interaction-curvature. All splits or standard classification decision trees will select the split predictor that maximizes the split-criterion gain over all possible splits of all predictors. Curvature selects the split predictor that minimizes the \(p\)-value of chi-square tests of independence between each predictor and the response. Training speed is similar to standard classification decision tree. Finally, interaction-curvature will choose the split predictor that minimizes the \(p\)-value of chi-square tests of independence between each predictor and the response, and that minimizes the \(p\)-value of a chi-square test of independence between each pair of predictors and response. Training speed can be slower than standard classification decision tree [34; 35; 36].