## 3 Research Design and Procedure
### Proposed Methodology (LADTree)  
The error threshold for creating regression trees is established using the Least Absolute Deviation (LAD) method, but Logical Analysis of Data provides an alternate classification methodology in the optimization literature. In LAD, a binary classifier is created by learning logical phrases that successfully differentiate positive and negative samples in a dataset [40,41]. The LAD model's central premise is that a binary point covered by positive patterns but not negative ones is considered positive, and vice versa for negative patterns. A LAD model is built by creating a wide collection of patterns and choosing a subset that matches these assumptions while ensuring that each pattern meets particular prevalence and homogeneity requirements. LADTree, a binary target variable classifier, learns logical expressions to differentiate between positive and negative samples, employs a logistic strategy for multiclass alternating decision tree generation, and can handle more than two class inputs. It also performs additive logistic regression [42,43]. The overall procedure of the LADTree is presented in Algorithm 1. ```
Input: - Dataset: A set of instances with features and class labels Output: - Decision tree model for classification
1. Start
2. Check if the stopping criteria for tree construction are met for the current dataset. 3. If stopping criteria are met:  a. Create a leaf node for the current dataset containing the majority class. b. Return the created leaf node. 4. Else:  a. Find  the best split for the current dataset using logistic regression. b. If no optimal split is found:  i. Create a leaf node for the current dataset containing the majority class. ii. Return the created leaf node. c. Else:  i. Split the dataset into left and right subsets based on the best split. ii. Recursively apply the LADTree algorithm to the left and right subsets. iii. Create a decision node with the best split and its corresponding child nodes. iv. Return the created decision node. 5. End
```  
**Algorithm 1**LADTree  
The offered algorithm describes how to build a decision tree model for classification using the LADTree technique. It begins by determining if the halting requirements for tree building are fulfilled for the current dataset. If the requirements are satisfied, the algorithm generates a leaf node with the majority class and returns it. Otherwise, it applies logistic regression to determine the appropriate split for the dataset. If no optimal split is discovered, a leaf node with the majority class is generated and returned. If an optimum split is discovered, the dataset is partitioned into left and right subsets according to this split. The LADTree method is then performed iteratively on each subset, resulting in decision nodes with the best split and their child nodes. This procedure continues until each subset'sstopping conditions are fulfilled, resulting in a decision tree model for categorization. The tree-stopping criteria, finding the best split, splitting the dataset, and calculating deviance are presented in Algorithm 2:  
```
1. Determine the stopping criteria for tree construction (e.g., maximum depth, minimum samples per node). 2. Return true if the stopping criteria are met; otherwise, return false. Function: FindBestSplit(Dataset)
1. Initialize best_split as null and best_deviance as infinity. 2. For each feature in the dataset: 1. For each value in the feature: 1. Split the dataset into left and right subsets. 2. Calculate the deviance using logistic regression. 3. If the calculated deviance is less than the best_deviance: 1. Update best_deviance with the calculated deviance. 2. Update best_split with the current feature and value. 3. Return the best_split. Function: SplitDataset(Dataset, feature, value)
1. Initialize left_subset and right_subset as empty subsets. 2. For each instance in the dataset: 1. If the feature value of the instance is less than or equal to the given value: 1. Add the instance to the left_subset. 2. Else: 1. Add the instance to the right_subset. 3.