Graph Coloring using Graph Convolutional Network (GCN)

This project is about graph coloring using Neural Networks (NNs) applied to graph-structured data, specifically the Cora citation network dataset. The project implements a Graph Convolutional Network (GCN) model to predict node classes (colors) for graph coloring, with an emphasis on hyperparameter tuning, early stopping, and learning rate scheduling.

Key Components of the Project:

1. Graph Data:

   • The project uses the Cora dataset, which is a citation network consisting of 2708 scientific papers (nodes) that are linked by citation relationships (edges).
   • The nodes have feature vectors representing the content of the papers, and the edges represent citation links between them.
   • Each node (paper) belongs to one of the predefined classes (or categories), and the task is to predict these classes using the graph structure and node features.

2. Model Architecture:

   • GCN (Graph Convolutional Network):
     • The core of the model is a two-layer GCN, implemented using GCNConv layers from PyTorch Geometric. These layers learn node representations based on both the node features and the graph structure (edges).
     • The output layer uses log-softmax activation, which is appropriate for multi-class classification (coloring nodes in different categories).
   • GraphSAGE (Graph Sample and Aggregation):
     • A second model variant, GraphSAGE, is implemented for comparison. GraphSAGE is a more advanced method for learning node embeddings by aggregating information from a node's neighbors.

3. Training Loop:

   • The training procedure involves optimizing the model using cross-entropy loss for multi-class classification and the Adam optimizer.
   • The training loop includes functionality for early stopping to avoid overfitting. This is controlled by the EarlyStopping class, which monitors the validation accuracy and stops the training if the accuracy doesn't improve for a specified number of epochs.
   • The learning rate scheduler (ReduceLROnPlateau) adjusts the learning rate based on the loss to prevent overshooting and improve convergence.

4. Hyperparameter Tuning:

   • The project uses grid search to experiment with different hyperparameter configurations such as learning rate, hidden dimension size, dropout rate, and the number of epochs.
   • The grid search is done via the ParameterGrid from sklearn.model_selection to evaluate the model on different combinations of parameters and identify the best set of hyperparameters.

5. Evaluation:

   • After training, the model's performance is evaluated using accuracy on a test set (nodes that were not part of the training).
   • The performance is also evaluated using classification report and confusion matrix, providing detailed metrics like precision, recall, and F1-score for each class (color).

6. Graph Visualization:

   • The final output is a visualization of the Cora citation graph, where nodes are colored according to the predicted class (color) for each paper.
   • The graph is visualized using NetworkX and matplotlib. The nodes are positioned using a spring layout, which is a force-directed layout algorithm that spaces nodes based on their connectivity in the graph.
   • The pred variable holds the predicted class (color) for each node, and these colors are used in the plot.

7. Model Saving and Loading:

   • The trained model is saved to a file using torch.save(), allowing it to be loaded later for inference or further training using model.load_state_dict().

High-Level Project Workflow:

1. Data Loading: Load the Cora dataset and inspect its structure, including the number of nodes, edges, and features.
2. Model Definition: Define the GCN and GraphSAGE models using PyTorch and PyTorch Geometric.
3. Training and Hyperparameter Tuning: Train the model with different hyperparameter configurations using grid search, learning rate scheduling, and early stopping.
4. Evaluation: After training, evaluate the model's performance using accuracy, classification metrics, and confusion matrix.
5. Visualization: Visualize the graph with node colors based on the predicted classes.

GitHub Project Explanation:

This repository likely contains the code for the above steps, and each script might be structured as follows:

• Data loading and exploration: Load and inspect the Cora dataset.
• Model definition: Define the GCN and GraphSAGE models and other necessary components (e.g., optimizer, loss function, etc.).
• Training: Implement the training loop, validation, early stopping, and learning rate scheduling.
• Evaluation: Compute and print the evaluation metrics and confusion matrix.
• Visualization: Generate a visualization of the graph, showing the node classifications (colors).
• Hyperparameter search: Implement grid search for hyperparameter optimization.

This project is a good example of applying deep learning models to graph-structured data and can be extended to other graph coloring problems or graph classification tasks.