## 4 Proposed Methodology for Rumor Detection
### Machine Learning for Rumor Detection  
#### 4.3.1 Data Mining Classifier  
The Support Vector Machine (SVM), which is available in numerous kernel functions, is another architecture for binary classification issues. The main objective of SVM in this research is generating a hyper plane based on features set for data points classification [27; 28]. In this research, our main objective is to find the best hyper plan that classifies the data point with the greatest margin. Ref. [29] explains the mathematical concept of the cost function for the SVM model.  
\[h(\theta)=1/2\Sigma\theta_{j}^{2} \tag{5}\]  
such that  
\[\theta^{T}x^{(i)}>=1,y^{(i)}=1\theta^{T}x^{(i)}<=-1,y^{(i)}=0 \tag{6}\]  
A very well-known supervised machine learning model for classification is SVM. It has a reputation for being extremely accurate while consuming very little computing power. It is based on the hyper plane principle. This approach separates the data into distinct classes by inserting hyper planes in N-dimensional space. The results are stated in Section 5.1.1.  
Random forest is an enhanced version of decision tree that is used for supervised learning. Random forest is characterized by a significant number of decision trees that are used to predict the target class. This prediction criterion is based on the highest number of votes. When we compare the random forest with other classifiers, its error rate is low due to the lack of proper connection between trees [30]. In this research, we train our random forest model by using different parameters, i.e., different number of predictions that are used in the search algorithm to obtain the optimal solution or model that can predict the outcome values accurately. We use the Gini index as a cost function to estimate a split in the dataset for the classification task. The Gini index is determined by subtracting one from the total squared probability of each class.  
\[G_{i}nd=1-\sum_{i=1}^{c}P(i)^{2} \tag{7}\]  
Random forest can be thought of as a collection of trees that work together as an ensemble model. This classifier creates a number of decisions trees and then uses a majority vote to determine the final prediction. This is more effective than decision trees since the decision trees work together as a group and correct each other's mistakes. Each tree in a random forest is trained using different bits of data and features bagging. As a result, the trees are unrelated to one another.  
A logistic regression algorithm is used to classify the text into a binary class that deals with large number of features because it provides a straightforward equation for classifying problems into a binary class [31]. To obtain the best outcome for all datasets, we use these equations and perform a hyper parameter adjustment. The logistic regression hypothesis function is a mathematical function that calculates the probability of a certain event occurring. By using a sigmoid function, the output value of logistic regression is transformed into a probability value. The cost function is computed as follows:  
\[h\theta(X)=1/1+e^{-}(\beta_{0}+\beta_{1}X) \tag{8}\]  
\[\{Cost(h_{\theta}(x))y=1-log(1-h_{\theta}(x)),y=0\} \tag{9}\]  
Gaussian naive Bayes is a more advanced version of naive Bayes. All variables in naive Bayes must be categorical. However, the data used in this study include numeric data. As a result, Gaussian naive Bayes is used, which assumes that the data are Gaussian. This classifier is also chosen since naive Bayes is often regarded as one of the most effective classifier models. This classifier employs the partial t technique, which is advantageous in large datasets because it takes chunks of data into account when training the classifier.