Train a Hypergraph Networks with Hyperedge Neurons (HNHN)#
In this notebook, we will create and train a Hypergraph Networks with Hyperedge Neurons in the hypergraph domain, as proposed in the paper by Dong et al. : HNHN: Hypergraph networks with hyperedge neurons (2020).
We train the model to perform binary node classification using the KarateClub benchmark dataset.
The equations of one layer of this neural network are given by:
🟥 \(\quad m_{y \rightarrow x}^{(0 \rightarrow 1)} = \sigma((B_1^T \cdot W^{(0)})_{xy} \cdot h_y^{t,(0)} \cdot \Theta^{t,(0)} + b^{t,(0)})\)
🟥 \(\quad m_{y \rightarrow x}^{(1 \rightarrow 0)} = \sigma((B_1 \cdot W^{(1)})_{xy} \cdot h_y^{t,(1)} \cdot \Theta^{t,(1)} + b^{t,(1)})\)
🟧 \(\quad m_x^{(0 \rightarrow 1)} = \sum_{y \in \mathcal{B}(x)} m_{y \rightarrow x}^{(0 \rightarrow 1)}\)
🟧 \(\quad m_x^{(1 \rightarrow 0)} = \sum_{y \in \mathcal{C}(x)} m_{y \rightarrow x}^{(1 \rightarrow 0)}\)
🟩 \(\quad m_x^{(0)} = m_x^{(1 \rightarrow 0)}\)
🟩 \(\quad m_x^{(1)} = m_x^{(0 \rightarrow 1)}\)
🟦 \(\quad h_x^{t+1,(0)} = m_x^{(0)}\)
🟦 \(\quad h_x^{t+1,(1)} = m_x^{(1)}\)
Where the notations are defined in Papillon et al : Architectures of Topological Deep Learning: A Survey of Topological Neural Networks (2023).
[1]:
"""
This module contains the HNHN class for hypergraph-based neural networks.
The HNHN class implements a specific hypergraph-based neural network architecture
used for solving certain types of problems.
Author: Your Name
"""
import numpy as np
import torch
import torch_geometric.datasets as geom_datasets
from torch_geometric.utils import to_undirected
from topomodelx.nn.hypergraph.hnhn import HNHN
torch.manual_seed(0)
If GPU’s are available, we will make use of them. Otherwise, this will run on CPU.
[2]:
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
print(device)
cuda
Pre-processing#
Import data#
The first step is to import the dataset, Cora, a benchmark classification datase. We then lift the graph into our domain of choice, a hypergraph.
[3]:
cora = geom_datasets.Planetoid(root="tmp/", name="cora")
data = cora.data
x_0s = data.x
y = data.y
edge_index = data.edge_index
train_mask = data.train_mask
val_mask = data.val_mask
test_mask = data.test_mask
/usr/local/lib/python3.11/site-packages/torch_geometric/data/in_memory_dataset.py:284: UserWarning: It is not recommended to directly access the internal storage format `data` of an 'InMemoryDataset'. If you are absolutely certain what you are doing, access the internal storage via `InMemoryDataset._data` instead to suppress this warning. Alternatively, you can access stacked individual attributes of every graph via `dataset.{attr_name}`.
warnings.warn(msg)
Define neighborhood structures and lift into hypergraph domain.#
Now we retrieve the neighborhood structure (i.e. their representative matrice) that we will use to send messges from node to hyperedges. In the case of this architecture, we need the boundary matrix (or incidence matrix) \(B_1\) with shape \(n_\text{nodes} \times n_\text{edges}\).
In citation Cora dataset we lift graph structure to the hypergraph domain by creating hyperedges from 1-hop graph neighbourhood of each node.
[4]:
# Ensure the graph is undirected (optional but often useful for one-hop neighborhoods).
edge_index = to_undirected(edge_index)
# Create a list of one-hop neighborhoods for each node.
one_hop_neighborhoods = []
for node in range(data.num_nodes):
# Get the one-hop neighbors of the current node.
neighbors = data.edge_index[1, data.edge_index[0] == node]
# Append the neighbors to the list of one-hop neighborhoods.
one_hop_neighborhoods.append(neighbors.numpy())
# Detect and eliminate duplicate hyperedges.
unique_hyperedges = set()
hyperedges = []
for neighborhood in one_hop_neighborhoods:
# Sort the neighborhood to ensure consistent comparison.
neighborhood = tuple(sorted(neighborhood))
if neighborhood not in unique_hyperedges:
hyperedges.append(list(neighborhood))
unique_hyperedges.add(neighborhood)
Additionally we print the statictis associated with obtained incidence matrix
[5]:
# Calculate hyperedge statistics.
hyperedge_sizes = [len(he) for he in hyperedges]
min_size = min(hyperedge_sizes)
max_size = max(hyperedge_sizes)
mean_size = np.mean(hyperedge_sizes)
median_size = np.median(hyperedge_sizes)
std_size = np.std(hyperedge_sizes)
num_single_node_hyperedges = sum(np.array(hyperedge_sizes) == 1)
# Print the hyperedge statistics.
print("Hyperedge statistics: ")
print("Number of hyperedges without duplicated hyperedges", len(hyperedges))
print(f"min = {min_size}, ")
print(f"max = {max_size}, ")
print(f"mean = {mean_size}, ")
print(f"median = {median_size}, ")
print(f"std = {std_size}, ")
print(f"Number of hyperedges with size equal to one = {num_single_node_hyperedges}")
Hyperedge statistics:
Number of hyperedges without duplicated hyperedges 2581
min = 1,
max = 168,
mean = 4.003099573808601,
median = 3.0,
std = 5.327622607829558,
Number of hyperedges with size equal to one = 412
Construct incidence matrix
[6]:
max_edges = len(hyperedges)
incidence_1 = np.zeros((x_0s.shape[0], max_edges))
for col, neighibourhood in enumerate(hyperedges):
for row in neighibourhood:
incidence_1[row, col] = 1
assert all(incidence_1.sum(0) > 0) is True, "Some hyperedges are empty"
assert all(incidence_1.sum(1) > 0) is True, "Some nodes are not in any hyperedges"
incidence_1 = torch.Tensor(incidence_1).to_sparse_coo()
Create the Neural Network#
Define the network that initializes the base model and sets up the readout operation. Different downstream tasks might require different pooling procedures.
[7]:
class Network(torch.nn.Module):
"""Network class that initializes the base model and readout layer.
Base model parameters:
----------
Reqired:
in_channels : int
Dimension of the input features.
hidden_channels : int
Dimension of the hidden features.
Optitional:
**kwargs : dict
Additional arguments for the base model.
Readout layer parameters:
----------
out_channels : int
Dimension of the output features.
task_level : str
Level of the task. Either "graph" or "node".
"""
def __init__(
self, in_channels, hidden_channels, out_channels, task_level="graph", **kwargs
):
super().__init__()
# Define the model
self.base_model = HNHN(
in_channels=in_channels, hidden_channels=hidden_channels, **kwargs
)
# Readout
self.linear = torch.nn.Linear(hidden_channels, out_channels)
self.out_pool = task_level == "graph"
def forward(self, x_0):
# Base model
x_0, x_1 = self.base_model(x_0)
# Pool over all nodes in the hypergraph
x = torch.max(x_0, dim=0)[0] if self.out_pool is True else x_0
return self.linear(x)
Initialize the model
[8]:
# Base model hyperparameters
in_channels = x_0s.shape[1]
hidden_channels = 128
n_layers = 1
mlp_num_layers = 1
# Readout hyperparameters
out_channels = torch.unique(y).shape[0]
task_level = "graph" if out_channels == 1 else "node"
model = Network(
in_channels=in_channels,
hidden_channels=hidden_channels,
out_channels=out_channels,
n_layers=n_layers,
incidence_1=incidence_1,
task_level=task_level,
).to(device)
Train the Neural Network#
We specify the model, the loss, and an optimizer.
[9]:
# Optimizer and loss
opt = torch.optim.Adam(model.parameters(), lr=0.01)
# Categorial cross-entropy loss
loss_fn = torch.nn.CrossEntropyLoss()
# Accuracy
def acc_fn(y, y_hat):
return (y == y_hat).float().mean()
[10]:
x_0s = torch.tensor(x_0s)
x_0s, incidence_1, y = (
x_0s.float().to(device),
incidence_1.float().to(device),
torch.tensor(y, dtype=torch.long).to(device),
)
/tmp/ipykernel_96287/1422611997.py:1: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).
x_0s = torch.tensor(x_0s)
/tmp/ipykernel_96287/1422611997.py:5: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).
torch.tensor(y, dtype=torch.long).to(device),
The following cell performs the training, looping over the network for a low amount of epochs. We keep training minimal for the purpose of rapid testing.
Note: The number of epochs below have been kept low to facilitate debugging and testing. Real use cases should likely require more epochs.
[11]:
test_interval = 5
num_epochs = 5
epoch_loss = []
for epoch_i in range(1, num_epochs + 1):
model.train()
opt.zero_grad()
# Extract edge_index from sparse incidence matrix
y_hat = model(x_0s)
loss = loss_fn(y_hat[train_mask], y[train_mask])
loss.backward()
opt.step()
epoch_loss.append(loss.item())
if epoch_i % test_interval == 0:
model.eval()
y_hat = model(x_0s)
loss = loss_fn(y_hat[train_mask], y[train_mask])
print(f"Epoch: {epoch_i} ")
print(
f"Train_loss: {np.mean(epoch_loss):.4f}, acc: {acc_fn(y_hat[train_mask].argmax(1), y[train_mask]):.4f}",
flush=True,
)
loss = loss_fn(y_hat[val_mask], y[val_mask])
print(
f"Val_loss: {loss:.4f}, Val_acc: {acc_fn(y_hat[val_mask].argmax(1), y[val_mask]):.4f}",
flush=True,
)
loss = loss_fn(y_hat[test_mask], y[test_mask])
print(
f"Test_loss: {loss:.4f}, Test_acc: {acc_fn(y_hat[test_mask].argmax(1), y[test_mask]):.4f}",
flush=True,
)
Epoch: 5
Train_loss: 1.1216, acc: 0.9929
Val_loss: 0.8693, Val_acc: 0.7340
Test_loss: 0.8030, Test_acc: 0.7570
Epoch: 10
Train_loss: 0.5751, acc: 1.0000
Val_loss: 1.6032, Val_acc: 0.7140
Test_loss: 1.3768, Test_acc: 0.7370
Epoch: 15
Train_loss: 0.3835, acc: 1.0000
Val_loss: 2.6746, Val_acc: 0.7120
Test_loss: 2.2858, Test_acc: 0.7320
Epoch: 20
Train_loss: 0.2876, acc: 1.0000
Val_loss: 3.5548, Val_acc: 0.7160
Test_loss: 3.0300, Test_acc: 0.7310
Epoch: 25
Train_loss: 0.2301, acc: 1.0000
Val_loss: 4.1969, Val_acc: 0.7120
Test_loss: 3.5745, Test_acc: 0.7310
Epoch: 30
Train_loss: 0.1917, acc: 1.0000
Val_loss: 4.6384, Val_acc: 0.7140
Test_loss: 3.9496, Test_acc: 0.7310