Dynamic Graph Convolutional Filters

PyTorch implementation of the Dynamic Graph Convolutional Filter (DGCF) layer presented in "Adaptive Filters in Graph Convolutional Neural Networks", Pattern Recognition (2023)

Params:

• n_nodes, int: number of nodes of the input graphs
• kernel_size, int: number of neighbors for convolution
• neighborhoods, torch.Tensor: matrix $N$ with dimensions (n_nodes, kernel_size) where the entry $N_{ij}$ denotes for the $i$'s $j$-th closest neighbor.
• in_channels, int: number of input channels for each node
• out_channels, int: number of output channels for each node
• filter_generating_network, nn.Module: filter generating network. It receives in input a feature vector resulting by the vectorization of all the nodes' features. It returns the vectorized weights (whose dimension is out_channels * in_channels * kernel_size [+ out_channels if bias is dynamic]).
• bias, string (default, 'static'):, whether the layer uses a bias vector. It can be:
• • static, whether the layer uses a single bias vector for each input
• • dynamic, whether the biases are generated from the filter_generating_network. In such case, the biases will be determined by the last [+ out_channels] weights generated from the filter_generating network.
• bias_initializer, Callable: Initializer for the bias vector (zeros by default. Use nn.init.* inizializations)

Input shape: (batch_size, n_nodes, in_channels)
Output shape: (batch_size, n_nodes, out_channels)

Usage

>>> ...
>>> # Let's consider 'x' as a batch of 20 graphs with 5 nodes and 3 input channels per node
>>> ...
>>> print(x.size())
torch.Size([20, 5, 3])
>>> out_features = 1
>>> # Let's define the dynamic-filter network's architecture
>>> filter_generating_net = nn.Sequential(
>>> ... nn.Linear(in_channels * n_nodes, 50),
>>> ... nn.ReLU(),
>>> ... nn.Linear(50, out_channels * in_channels * kernel_size)
>>> )
>>> f = DGCF(n_nodes, kernel_size, neighborhoods, in_channels, out_channels, filter_generating_net)
>>> y = f(x)
>>> print(y.size())
torch.Size([20, 5, 1])

Example of usage on MNIST

An example of usage is reported in the example_mnist.py script, where it is reported the setting used for the experiments made on the MNIST dataset reported in Section 4.1. Additionally, a pretrained model on MNIST is also uploaded (pretrained_MNIST.pt).

Citing

@article{apicella2023adaptive,
  title={Adaptive filters in graph convolutional neural networks},
  author={Apicella, Andrea and Isgr{\`o}, Francesco and Pollastro, Andrea and Prevete, Roberto},
  journal={Pattern Recognition},
  volume={144},
  pages={109867},
  year={2023},
  publisher={Elsevier}
}