图神经网络
此笔记本说明了如何使用 图神经网络 在图中执行节点分类。
[1]:
from IPython.display import SVG
[2]:
import numpy as np
from scipy import sparse
[3]:
from sknetwork.data import art_philo_science
from sknetwork.classification import get_accuracy_score
from sknetwork.gnn import GNNClassifier
from sknetwork.visualization import visualize_graph
带特征的图
让我们加载 art_philo_science 玩具数据集。它包含 30 篇维基百科文章的精选，以及它们之间的链接。每篇文章由其摘要中使用的一些词语描述，这些词语来自一个包含 11 个词语的列表。每篇文章都属于以下 3 个类别之一：艺术、哲学或科学。
目标是从其他文章的类别（训练集）中检索一些文章（测试集）的类别。
[4]:
graph = art_philo_science(metadata=True)
adjacency = graph.adjacency
features = graph.biadjacency
names = graph.names
names_features = graph.names_col
names_labels = graph.names_labels
labels_true = graph.labels
position = graph.position
[5]:
adjacency
[5]:
<30x30 sparse matrix of type '<class 'numpy.bool_'>'
with 240 stored elements in Compressed Sparse Row format>
[6]:
print(names)
['Isaac Newton' 'Albert Einstein' 'Carl Linnaeus' 'Charles Darwin'
'Ptolemy' 'Gottfried Wilhelm Leibniz' 'Carl Friedrich Gauss'
'Galileo Galilei' 'Leonhard Euler' 'John von Neumann' 'Leonardo da Vinci'
'Richard Wagner' 'Ludwig van Beethoven' 'Bob Dylan' 'Igor Stravinsky'
'The Beatles' 'Wolfgang Amadeus Mozart' 'Richard Strauss' 'Raphael'
'Pablo Picasso' 'Aristotle' 'Plato' 'Augustine of Hippo' 'Thomas Aquinas'
'Immanuel Kant' 'Bertrand Russell' 'David Hume' 'René Descartes'
'John Stuart Mill' 'Socrates']
[7]:
print(len(names))
30
[8]:
features
[8]:
<30x11 sparse matrix of type '<class 'numpy.int64'>'
with 101 stored elements in Compressed Sparse Row format>
[9]:
print(names_features)
['contribution' 'theory' 'invention' 'time' 'modern' 'century' 'study'
'logic' 'school' 'author' 'compose']
[10]:
len(names_features)
[10]:
11
[11]:
print(names_labels)
['science' 'arts' 'philosophy']
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# Number of labels
n_labels = len(set(labels_true))
GCN
默认的 GNN 是一个空间图卷积网络 (GCN)。我们在这里使用单个隐藏层。可以通过参数 dims（维度列表）指定更多隐藏层。
[13]:
# GNN classifier with a single hidden layer
hidden_dim = 5
gnn = GNNClassifier(dims=[hidden_dim, n_labels],
layer_types='Conv',
activations='ReLu',
verbose=True)
[14]:
print(gnn)
GNNClassifier(
Convolution(layer_type: conv, out_channels: 5, activation: ReLu, use_bias: True, normalization: both, self_embeddings: True)
Convolution(layer_type: conv, out_channels: 3, activation: Cross entropy, use_bias: True, normalization: both, self_embeddings: True)
)
[15]:
# Training set
labels = labels_true.copy()
np.random.seed(42)
train_mask = np.random.random(size=len(labels)) < 0.5
labels[train_mask] = -1
[16]:
# Training
labels_pred = gnn.fit_predict(adjacency, features, labels, n_epochs=200, random_state=42)
In epoch 0, loss: 1.053, train accuracy: 0.462
In epoch 20, loss: 0.834, train accuracy: 0.692
In epoch 40, loss: 0.819, train accuracy: 0.692
In epoch 60, loss: 0.831, train accuracy: 0.692
In epoch 80, loss: 0.839, train accuracy: 0.692
In epoch 100, loss: 0.839, train accuracy: 0.692
In epoch 120, loss: 0.825, train accuracy: 0.692
In epoch 140, loss: 0.771, train accuracy: 0.769
In epoch 160, loss: 0.557, train accuracy: 1.000
In epoch 180, loss: 0.552, train accuracy: 1.000
[17]:
# History for each training epoch
gnn.history_.keys()
[17]:
dict_keys(['loss', 'train_accuracy'])
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# Accuracy on test set
test_mask = ~train_mask
get_accuracy_score(labels_true[test_mask], labels_pred[test_mask])
[18]:
1.0
[19]:
# Visualization
image = visualize_graph(adjacency, position=position, names=names, labels=labels_pred)
SVG(image)
[19]:
[20]:
# probability distribution over labels
probs = gnn.predict_proba()
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label = 1
scores = probs[:, label]
[22]:
# Visualization
image = visualize_graph(adjacency, position=position, names=names, scores=scores)
SVG(image)
[22]:
GraphSAGE
另一个可用的 GNN 是 GraphSAGE。
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# GraphSAGE layers
gnn = GNNClassifier(dims=[5, 3], layer_types='Sage')
[24]:
print(gnn)
GNNClassifier(
Convolution(layer_type: sage, out_channels: 5, activation: ReLu, use_bias: True, normalization: left, self_embeddings: True, sample_size: 25)
Convolution(layer_type: sage, out_channels: 3, activation: Cross entropy, use_bias: True, normalization: left, self_embeddings: True, sample_size: 25)
)
[25]:
# Training
labels_pred = gnn.fit_predict(adjacency, features, labels, n_epochs=200, random_state=42)
[26]:
# Accuracy on test set
test_mask = ~train_mask
get_accuracy_score(labels_true[test_mask], labels_pred[test_mask])
[26]:
1.0
[27]:
# Parameters of the GNN
weights = [layer.weight for layer in gnn.layers]
biases = [layer.bias for layer in gnn.layers]
[28]:
[weight.shape for weight in weights]
[28]:
[(11, 5), (5, 3)]
[29]:
[bias.shape for bias in biases]
[29]:
[(1, 5), (1, 3)]
[30]:
# probability distribution over labels
probs = gnn.predict_proba()
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label = 1
scores = probs[:, label]
[32]:
# Visualization
image = visualize_graph(adjacency, position=position, names=names, scores=scores)
SVG(image)
[32]:
[33]:
# Parameters of the GNN
weights = [layer.weight for layer in gnn.layers]
biases = [layer.bias for layer in gnn.layers]
[34]:
[weight.shape for weight in weights]
[34]:
[(11, 5), (5, 3)]
[35]:
[bias.shape for bias in biases]
[35]:
[(1, 5), (1, 3)]
[36]:
# probability distribution over labels
probs = gnn.predict_proba()
[37]:
label = 1
scores = probs[:, label]
[38]:
# Visualization
image = visualize_graph(adjacency, position=position, names=names, scores=scores)
SVG(image)
[38]:
