# Big Data-Driven Deep Learning Ensembler for DDoS Attack Detection
## 3 Proposed System Model
### Feature Transformation and Mapping  
Refining the data for improved performance and machine-learning model interpretability requires data transformation and mapping. The procedures involved are taking temporal properties of the data, mapping features to relevant spaces, and lowering the dimensionality of the data.  
To reduce the amount of features in a dataset while keeping important information, dimensionality reduction is an effective strategy. We used PCA-LLP (Principal Component Analysis with Locality Preserving Projection) to simplify big datasets like IoT-23 so they could be processed quickly without losing vital features. Particularly useful for dealing with the high-dimensional data typical of IoT networks, PCA-LLP simplifies data by lowering its complexity while preserving crucial linkages between data points.  
Despite its effectiveness in capturing data variation, classical Principal Component Analysis (PCA) fails to maintain local structure, particularly in non-linear datasets. By including LPP (Locality Preserving Projection), we improve PCA's performance and make it more applicable to non-linear datasets by maintaining links between adjacent data points. This is how PCA and LPP define their objective functions:  
* Traditional PCA: optimizes the estimated space variance. Objective function is [31] \[\max_{\mathbf{U}}\operatorname{Var}(\mathbf{XU})\] (6)
* LPP: Reduction of reconstruction error is achieved by considering the relationships between adjacent pieces. Enhanced objective function is [31]. \[\min_{\mathbf{V}}\sum_{i=1}^{N}\|\mathbf{x}_{i}-\sum_{j=1}^{N}\mathbf{M}_{ij} \mathbf{v}_{j}\|^{2}\] (7)  
Improved PCA-LLP makes better dimensionality reduction possible with preserved critical data linkages. This technique increases computational efficiency in big datasets by conserving local structures using LPP.  
Feature mapping transforms features into a space that better reflects the fundamental patterns in the data.  
**Temporal mapping:** Temporal mapping is a technique used to capture the relationships between events that occur over time in a dataset [32]. This is particularly important for analyzing time-series data and sequential data.  
**Data profiling:** This step examines the dataset's properties and focuses on any constraints that can reduce the model's performance. In addition, the linkages between traits can be better understood using correlation analysis, which analyzes the relationship exactly. Class imbalance detection allows us to identify instances of unequal distributions of classes, which may have a major impact on how well classification models function. Calculating the frequency of each class in the target variable is the first step in class distribution analysis.  
\[\text{Frequency}(d)=\frac{\sum_{i=1}^{Q}I(w_{i}=d)}{Q} \tag{8}\]  
The equation \(\text{Frequency}(d)\) denotes the proportion of class \(d\) in the dataset. The symbol \(I\) represents the indicator function, \(w_{i}\) identifies the target variable, and \(Q\) signifies the total number of observations.  
Thorough data transformation, mapping, and profiling ensure that the datasets (IoT-23 and APA-DDoS) are adequately prepared for future machine-learning processes. This leads to improved accuracy and reliability in identifying DDoSA.