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://s3.us-east-2.amazonaws.com/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://s3.us-east-2.amazonaws.com/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

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://s3.us-east-2.amazonaws.com/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

The graph convolution operation is basically the same as that for graph convolutional network (GCN). To learn more, see the GCN tutorial). The only difference is that we replace \(h_{v}^{(l+1)} = \text{ReLU}\left(b^{(l)}+\sum_{u\in\mathcal{N}(v)}h_{u}^{(l)}W^{(l)}\right)\) by \(h_{v}^{(l+1)} = \text{ReLU}\left(b^{(l)}+\frac{1}{|\mathcal{N}(v)|}\sum_{u\in\mathcal{N}(v)}h_{u}^{(l)}W^{(l)}\right)\)

The replacement of summation by average is to balance nodes with different degrees. This gives a better performance for this experiment.

The self edges added in the dataset initialization allows you to include the original node feature \(h_{v}^{(l)}\) when taking the average.

import dgl.function as fn
import torch
import torch.nn as nn


# Sends a message of node feature h.
msg = fn.copy_src(src='h', out='m')

def reduce(nodes):
    """Take an average over all neighbor node features hu and use it to
    overwrite the original node feature."""
    accum = torch.mean(nodes.mailbox['m'], 1)
    return {'h': accum}

class NodeApplyModule(nn.Module):
    """Update the node feature hv with ReLU(Whv+b)."""
    def __init__(self, in_feats, out_feats, activation):
        super(NodeApplyModule, self).__init__()
        self.linear = nn.Linear(in_feats, out_feats)
        self.activation = activation

    def forward(self, node):
        h = self.linear(node.data['h'])
        h = self.activation(h)
        return {'h' : h}

class GCN(nn.Module):
    def __init__(self, in_feats, out_feats, activation):
        super(GCN, self).__init__()
        self.apply_mod = NodeApplyModule(in_feats, out_feats, activation)

    def forward(self, g, feature):
        # Initialize the node features with h.
        g.ndata['h'] = feature
        g.update_all(msg, reduce)
        g.apply_nodes(func=self.apply_mod)
        return g.ndata.pop('h')

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.functional as F


class Classifier(nn.Module):
    def __init__(self, in_dim, hidden_dim, n_classes):
        super(Classifier, self).__init__()

        self.layers = nn.ModuleList([
            GCN(in_dim, hidden_dim, F.relu),
            GCN(hidden_dim, hidden_dim, F.relu)])
        self.classify = nn.Linear(hidden_dim, n_classes)

    def forward(self, g):
        # For undirected graphs, in_degree is the same as
        # out_degree.
        h = g.in_degrees().view(-1, 1).float()
        for conv in self.layers:
            h = conv(g, h)
        g.ndata['h'] = h
        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 2.0744
Epoch 1, loss 1.9880
Epoch 2, loss 1.9160
Epoch 3, loss 1.8144
Epoch 4, loss 1.7113
Epoch 5, loss 1.6263
Epoch 6, loss 1.5470
Epoch 7, loss 1.4899
Epoch 8, loss 1.4006
Epoch 9, loss 1.3282
Epoch 10, loss 1.2855
Epoch 11, loss 1.2143
Epoch 12, loss 1.1741
Epoch 13, loss 1.1528
Epoch 14, loss 1.1222
Epoch 15, loss 1.0702
Epoch 16, loss 1.0186
Epoch 17, loss 0.9897
Epoch 18, loss 0.9511
Epoch 19, loss 0.9401
Epoch 20, loss 0.9237
Epoch 21, loss 0.8890
Epoch 22, loss 0.8684
Epoch 23, loss 0.8634
Epoch 24, loss 0.8439
Epoch 25, loss 0.8617
Epoch 26, loss 0.8358
Epoch 27, loss 0.8125
Epoch 28, loss 0.7969
Epoch 29, loss 0.7825
Epoch 30, loss 0.7848
Epoch 31, loss 0.7588
Epoch 32, loss 0.7611
Epoch 33, loss 0.7410
Epoch 34, loss 0.7363
Epoch 35, loss 0.7259
Epoch 36, loss 0.7275
Epoch 37, loss 0.7067
Epoch 38, loss 0.7123
Epoch 39, loss 0.7041
Epoch 40, loss 0.6913
Epoch 41, loss 0.6950
Epoch 42, loss 0.7057
Epoch 43, loss 0.6905
Epoch 44, loss 0.6792
Epoch 45, loss 0.6564
Epoch 46, loss 0.6581
Epoch 47, loss 0.6522
Epoch 48, loss 0.6677
Epoch 49, loss 0.6617
Epoch 50, loss 0.6743
Epoch 51, loss 0.6706
Epoch 52, loss 0.6749
Epoch 53, loss 0.6402
Epoch 54, loss 0.6449
Epoch 55, loss 0.6470
Epoch 56, loss 0.6384
Epoch 57, loss 0.6003
Epoch 58, loss 0.6411
Epoch 59, loss 0.6144
Epoch 60, loss 0.6248
Epoch 61, loss 0.6192
Epoch 62, loss 0.6015
Epoch 63, loss 0.5879
Epoch 64, loss 0.5878
Epoch 65, loss 0.5694
Epoch 66, loss 0.5668
Epoch 67, loss 0.5765
Epoch 68, loss 0.5895
Epoch 69, loss 0.5819
Epoch 70, loss 0.5663
Epoch 71, loss 0.5822
Epoch 72, loss 0.5422
Epoch 73, loss 0.5726
Epoch 74, loss 0.5460
Epoch 75, loss 0.5430
Epoch 76, loss 0.5285
Epoch 77, loss 0.5383
Epoch 78, loss 0.5483
Epoch 79, loss 0.5399

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: 67.5000%
Accuracy of argmax predictions on the test set: 75.000000%

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

https://s3.us-east-2.amazonaws.com/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://s3.us-east-2.amazonaws.com/dgl.ai/tutorial/batch/tsne_node2.png https://s3.us-east-2.amazonaws.com/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 27.221 seconds)

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