cave-g-f / GCN_Partitioning

Graph Partitoning Using Graph Convolutional Networks

GCN Partitioning

Graph Partitoning Using Graph Convolutional Networks as described in GAP: Generalizable Approximate Graph Partitioning Framework

Loss Backward Equations

To handle large graphs, the loss function is implemented using sparse torch tensors using a custom loss class.

If $Z = (Y / \Gamma)(1 - Y)^{T} \circ A$

where Y_{ij} is the probability of node i being in partition j.

$L = \sum_{A_{lm} \neq 0} Z_{lm}$

Then the gradients can be calculated by the equations:

$\frac{\partial z_{i \alpha}}{\partial y_{ij}} = A_{i \alpha} \left(\frac{\Gamma_{j} (1 - y_{\alpha j}) - y_{ij}(1 - y_{\alpha j})D_{i}}{\Gamma_{j}^{2}}\right)$

$\frac{\partial z_{\alpha i}}{\partial y_{ij}} = A_{\alpha i} \left(\frac{\Gamma_{j} (- y_{\alpha j}) - y_{\alpha j}(1 - y_{ij})D_{i}}{\Gamma_{j}^{2}}\right)$

$\frac{\partial z_{i^{'} \alpha}}{\partial y_{ij}} = A_{i^{'} \alpha} \left(\frac{(1 - y_{\alpha j}) y_{i^{'}j}D_{i}}{\Gamma_{j}^{2}}\right) ;;; i^{'}, \alpha \neq i$

Installation

Create a virtual environment using venv

python3 -m venv env

Source the virtual environment

source env/bin/activate

Use the package manager pip to install requirements.

pip install -r requirements.txt

Usage

python TrialModel.py

Limitations

Has only been tested on small custom graphs.

License

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Graph Partitoning Using Graph Convolutional Networks

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