# An Improved Random Forest Approach on GAN-Based Dataset Augmentation for Fog Observation
## 2 Data and Methodology
### Deep Learning Approaches: VGG16, VGG19, ResNet50, DenseNet169 and the Improved Random Forest  
VGG16 and VGG19 [26] are the two representative algorithms of the VGGNet, containing 13 and 16 convolutional layers, respectively. They extract features from input images using multiple 3 x 3 convolutional filters with a stride of 1 px. To accelerate the convergence of the model, the VGG series uses the ReLU activation function and applies max-pooling in the pooling layers to downsample the features. However, due to the deep network depth of the VGG models, the number of parameters is relatively large, which may lead to higher computational costs when handling complex image tasks.  
ResNet50 [27] effectively addresses the vanishing gradient problem in deep networks by introducing residual modules, making it possible to train deeper networks. ResNet50 includes 48 convolutional layers, 1 max-pooling layer, and 1 fully connected layer. Compared to the VGG series, the ResNet architecture is more complex, but it performs better in feature extraction and classification tasks, particularly in handling complex textures and detailed features in images.  
DenseNet169 [28] ensures efficient reuse of features at different levels by employing densely connected layers. DenseNet169 consists of 169 layers. Due to its densely connected nature, it significantly reduces the number of parameters and improves the training efficiency of the model. DenseNet has demonstrated strong classification capabilities and generalization abilities when processing high-resolution and diverse image data.  
Traditional Random Forest models make predictions by constructing multiple random decision trees, with each tree randomly selecting a subset of features from the input for training [29]. Through ensemble learning, the Random Forest model reduces the risk of overfitting associated with individual decision trees, thereby enhancing the model's stability.  
When observing fog concentration, the data often include various image features, resulting in high-dimensional and noisy data. This can negatively impact the performance of weak classifiers in traditional Random Forest models, leading to a decline in overall classification accuracy. To address the limitations of traditional Random Forest models in handling high-dimensional data and complex nonlinear relationships, a hybrid clustering-based method is introduced to optimize decision tree selection, improving the model's overall performance. The specific steps are as follows:  
1. Hierarchical Clustering. Initially, each decision tree is treated as an independent cluster. The Dunn index is used to calculate the similarity between any two decision trees, and the two clusters with the smallest similarity are merged. This process is repeated until the number of remaining clusters reaches a predetermined value. Then, the decision tree with the best classification performance is selected from each cluster to form a new Random Forest model.
2. K-Medoids Clustering. The cluster centers obtained from hierarchical clustering are used as the initial clusters for k-Medoids clustering. The similarity between the unclassified decision trees and each cluster center is calculated, and the decision trees are reassigned based on the nearest neighbor principle. Then, the decision tree with the best performance within each cluster is selected as the new cluster center. This process is repeated until the cluster centers stabilize or the maximum number of iterations is reached.
3. Model Training and Prediction: The preprocessed feature data are input into the improved Random Forest model for training. The model constructs a large number of decision trees, with each tree independently predicting the fog density. The final output is the average of the predictions from all decision trees.