Graph Classification Tutorial

Author: Mufei Li, Minjie Wang, Zheng Zhang.

In this tutorial, you learn how to use DGL to batch multiple graphs of variable size and shape. The tutorial also demonstrates training a graph neural network for a simple graph classification task.

Graph classification is an important problem with applications across many fields, such as bioinformatics, chemoinformatics, social network analysis, urban computing, and cybersecurity. Applying graph neural networks to this problem has been a popular approach recently. This can be seen in the following reserach references: Ying et al., 2018, Cangea et al., 2018, Knyazev et al., 2018, Bianchi et al., 2019, Liao et al., 2019, Gao et al., 2019).

Simple graph classification task

In this tutorial, you learn how to perform batched graph classification with DGL. The example task objective is to classify eight types of topologies shown here.

https://data.dgl.ai/tutorial/batch/dataset_overview.png

Implement a synthetic dataset data.MiniGCDataset in DGL. The dataset has eight different types of graphs and each class has the same number of graph samples.

from dgl.data import MiniGCDataset
import matplotlib.pyplot as plt
import networkx as nx
# A dataset with 80 samples, each graph is
# of size [10, 20]
dataset = MiniGCDataset(80, 10, 20)
graph, label = dataset[0]
fig, ax = plt.subplots()
nx.draw(graph.to_networkx(), ax=ax)
ax.set_title('Class: {:d}'.format(label))
plt.show()
../../_images/sphx_glr_4_batch_001.png

Form a graph mini-batch

To train neural networks efficiently, a common practice is to batch multiple samples together to form a mini-batch. Batching fixed-shaped tensor inputs is common. For example, batching two images of size 28 x 28 gives a tensor of shape 2 x 28 x 28. By contrast, batching graph inputs has two challenges:

  • Graphs are sparse.

  • Graphs can have various length. For example, number of nodes and edges.

To address this, DGL provides a dgl.batch() API. It leverages the idea that a batch of graphs can be viewed as a large graph that has many disjointed connected components. Below is a visualization that gives the general idea.

https://data.dgl.ai/tutorial/batch/batch.png

Define the following collate function to form a mini-batch from a given list of graph and label pairs.

import dgl
import torch

def collate(samples):
    # The input `samples` is a list of pairs
    #  (graph, label).
    graphs, labels = map(list, zip(*samples))
    batched_graph = dgl.batch(graphs)
    return batched_graph, torch.tensor(labels)

The return type of dgl.batch() is still a graph. In the same way, a batch of tensors is still a tensor. This means that any code that works for one graph immediately works for a batch of graphs. More importantly, because DGL processes messages on all nodes and edges in parallel, this greatly improves efficiency.

Graph classifier

Graph classification proceeds as follows.

https://data.dgl.ai/tutorial/batch/graph_classifier.png

From a batch of graphs, perform message passing and graph convolution for nodes to communicate with others. After message passing, compute a tensor for graph representation from node (and edge) attributes. This step might be called readout or aggregation. Finally, the graph representations are fed into a classifier \(g\) to predict the graph labels.

Graph convolution layer can be found in the dgl.nn.<backend> submodule.

from dgl.nn.pytorch import GraphConv

Readout and classification

For this demonstration, consider initial node features to be their degrees. After two rounds of graph convolution, perform a graph readout by averaging over all node features for each graph in the batch.

\[h_g=\frac{1}{|\mathcal{V}|}\sum_{v\in\mathcal{V}}h_{v}\]

In DGL, dgl.mean_nodes() handles this task for a batch of graphs with variable size. You then feed the graph representations into a classifier with one linear layer to obtain pre-softmax logits.

import torch.nn as nn
import torch.nn.functional as F

class Classifier(nn.Module):
    def __init__(self, in_dim, hidden_dim, n_classes):
        super(Classifier, self).__init__()
        self.conv1 = GraphConv(in_dim, hidden_dim)
        self.conv2 = GraphConv(hidden_dim, hidden_dim)
        self.classify = nn.Linear(hidden_dim, n_classes)

    def forward(self, g):
        # Use node degree as the initial node feature. For undirected graphs, the in-degree
        # is the same as the out_degree.
        h = g.in_degrees().view(-1, 1).float()
        # Perform graph convolution and activation function.
        h = F.relu(self.conv1(g, h))
        h = F.relu(self.conv2(g, h))
        g.ndata['h'] = h
        # Calculate graph representation by averaging all the node representations.
        hg = dgl.mean_nodes(g, 'h')
        return self.classify(hg)

Setup and training

Create a synthetic dataset of \(400\) graphs with \(10\) ~ \(20\) nodes. \(320\) graphs constitute a training set and \(80\) graphs constitute a test set.

import torch.optim as optim
from torch.utils.data import DataLoader

# Create training and test sets.
trainset = MiniGCDataset(320, 10, 20)
testset = MiniGCDataset(80, 10, 20)
# Use PyTorch's DataLoader and the collate function
# defined before.
data_loader = DataLoader(trainset, batch_size=32, shuffle=True,
                         collate_fn=collate)

# Create model
model = Classifier(1, 256, trainset.num_classes)
loss_func = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)
model.train()

epoch_losses = []
for epoch in range(80):
    epoch_loss = 0
    for iter, (bg, label) in enumerate(data_loader):
        prediction = model(bg)
        loss = loss_func(prediction, label)
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        epoch_loss += loss.detach().item()
    epoch_loss /= (iter + 1)
    print('Epoch {}, loss {:.4f}'.format(epoch, epoch_loss))
    epoch_losses.append(epoch_loss)

Out:

Epoch 0, loss 2.0134
Epoch 1, loss 1.9705
Epoch 2, loss 1.9592
Epoch 3, loss 1.9487
Epoch 4, loss 1.9404
Epoch 5, loss 1.9304
Epoch 6, loss 1.9173
Epoch 7, loss 1.8902
Epoch 8, loss 1.8661
Epoch 9, loss 1.8354
Epoch 10, loss 1.7988
Epoch 11, loss 1.7541
Epoch 12, loss 1.7064
Epoch 13, loss 1.6532
Epoch 14, loss 1.5961
Epoch 15, loss 1.5320
Epoch 16, loss 1.4739
Epoch 17, loss 1.4080
Epoch 18, loss 1.3555
Epoch 19, loss 1.3115
Epoch 20, loss 1.2553
Epoch 21, loss 1.2284
Epoch 22, loss 1.1879
Epoch 23, loss 1.1392
Epoch 24, loss 1.1008
Epoch 25, loss 1.0863
Epoch 26, loss 1.0588
Epoch 27, loss 1.0192
Epoch 28, loss 1.0084
Epoch 29, loss 1.0015
Epoch 30, loss 0.9698
Epoch 31, loss 0.9500
Epoch 32, loss 0.9264
Epoch 33, loss 0.9152
Epoch 34, loss 0.9167
Epoch 35, loss 0.8930
Epoch 36, loss 0.8751
Epoch 37, loss 0.8627
Epoch 38, loss 0.8501
Epoch 39, loss 0.8676
Epoch 40, loss 0.8461
Epoch 41, loss 0.8279
Epoch 42, loss 0.8193
Epoch 43, loss 0.8125
Epoch 44, loss 0.8046
Epoch 45, loss 0.7961
Epoch 46, loss 0.8058
Epoch 47, loss 0.7904
Epoch 48, loss 0.7734
Epoch 49, loss 0.7711
Epoch 50, loss 0.7741
Epoch 51, loss 0.8125
Epoch 52, loss 0.8182
Epoch 53, loss 0.7543
Epoch 54, loss 0.7546
Epoch 55, loss 0.7643
Epoch 56, loss 0.7440
Epoch 57, loss 0.7323
Epoch 58, loss 0.7355
Epoch 59, loss 0.7414
Epoch 60, loss 0.7471
Epoch 61, loss 0.7491
Epoch 62, loss 0.7340
Epoch 63, loss 0.7334
Epoch 64, loss 0.7185
Epoch 65, loss 0.7089
Epoch 66, loss 0.7077
Epoch 67, loss 0.7026
Epoch 68, loss 0.7152
Epoch 69, loss 0.6948
Epoch 70, loss 0.7152
Epoch 71, loss 0.6921
Epoch 72, loss 0.6943
Epoch 73, loss 0.6789
Epoch 74, loss 0.6990
Epoch 75, loss 0.6908
Epoch 76, loss 0.6847
Epoch 77, loss 0.6725
Epoch 78, loss 0.6787
Epoch 79, loss 0.6648

The learning curve of a run is presented below.

plt.title('cross entropy averaged over minibatches')
plt.plot(epoch_losses)
plt.show()
../../_images/sphx_glr_4_batch_002.png

The trained model is evaluated on the test set created. To deploy the tutorial, restrict the running time to get a higher accuracy (\(80\) % ~ \(90\) %) than the ones printed below.

model.eval()
# Convert a list of tuples to two lists
test_X, test_Y = map(list, zip(*testset))
test_bg = dgl.batch(test_X)
test_Y = torch.tensor(test_Y).float().view(-1, 1)
probs_Y = torch.softmax(model(test_bg), 1)
sampled_Y = torch.multinomial(probs_Y, 1)
argmax_Y = torch.max(probs_Y, 1)[1].view(-1, 1)
print('Accuracy of sampled predictions on the test set: {:.4f}%'.format(
    (test_Y == sampled_Y.float()).sum().item() / len(test_Y) * 100))
print('Accuracy of argmax predictions on the test set: {:4f}%'.format(
    (test_Y == argmax_Y.float()).sum().item() / len(test_Y) * 100))

Out:

Accuracy of sampled predictions on the test set: 62.5000%
Accuracy of argmax predictions on the test set: 67.500000%

The animation here plots the probability that a trained model predicts the correct graph type.

https://data.dgl.ai/tutorial/batch/test_eval4.gif

To understand the node and graph representations that a trained model learned, we use t-SNE, for dimensionality reduction and visualization.

https://data.dgl.ai/tutorial/batch/tsne_node2.png https://data.dgl.ai/tutorial/batch/tsne_graph2.png

The two small figures on the top separately visualize node representations after one and two layers of graph convolution. The figure on the bottom visualizes the pre-softmax logits for graphs as graph representations.

While the visualization does suggest some clustering effects of the node features, you would not expect a perfect result. Node degrees are deterministic for these node features. The graph features are improved when separated.

What’s next?

Graph classification with graph neural networks is still a new field. It’s waiting for people to bring more exciting discoveries. The work requires mapping different graphs to different embeddings, while preserving their structural similarity in the embedding space. To learn more about it, see How Powerful Are Graph Neural Networks? a research paper published for the International Conference on Learning Representations 2019.

For more examples about batched graph processing, see the following:

Total running time of the script: ( 0 minutes 20.617 seconds)

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