GraphSAGE（Graph Sample and Aggregated Embeddings）
GraphSAGE (Graph Sample and Aggregated Embeddings) is a graph embedding algorithm for learning node embeddings (vector representation) from graph data. By sampling and aggregating the local neighborhood information of nodes, it effectively learns the embedding of each node. This approach makes it possible to obtain high-performance embeddings for large graphs.
GraphSAGE, reported by Hamilton et al. in “Inductive Representation Learning on Large Graphs,” is an inductive embedding method for unknown or unobserved nodes and subgraphs, whereas conventional transductive embedding methods require all nodes to be visible during training. In contrast to conventional transductive methods, which require all nodes to be visible during training, this method provides inductive (from specific to general) embedding for unknown or unobserved nodes and subgraphs.
The main features and elements of GraphSAGE are described below.
1. sampling:
In learning the representation of the nodes of a graph, GraphSAGE does not use all the neighbors, but fixes the number of neighbors by sampling. and replaces the hash function in the WL isomorphism test with an aggregate of trainable neural nets.
GraphSAGE can use a variety of sampling strategies when sampling the neighbors around each node, such as random sampling or weighted sampling, whereby the local structural information of the nodes is obtained by sampling.
2. aggregation:
GraphSAGE updates the representation of its own nodes by aggregating the representations of neighboring nodes. Aggregation methods include averaging, pooling, and attention mechanisms (weighting of nodes to pay attention to).
The paper reports that K=2 is a good neighborhood distance for aggregation, and that anything more than that increases computation time very much more than a small performance gain. The paper experiments three types of aggregation methods: average, LSTM, a type of recursive neural network, and pooling, and reports that the performance of LSTM and pooling is slightly better than that of average, and that LSTM takes more computation time.
3. deep learning model:
GraphSAGE uses a multi-layered neural network to learn embeddings. At each layer, sampling and aggregation are alternated and the embedding is hierarchically updated to obtain a richer representation with this deep learning model.
4. application to non-homogeneous graphs:
GraphSAGE can also be applied to non-homogeneous graphs (where edges between different nodes have different meanings). By assigning different weights to each edge, it is possible to learn embeddings for different types of edges.
5. application to various applications:
GraphSAGE can be applied to a variety of graph data-related tasks such as node clustering, classification, link prediction, and recommendation. In particular, it is widely used in areas such as social network analysis and web page link graph analysis.
Based on the obtained representations, the paper reports node and graph classification using citation networks, Reddit posting networks, and protein interaction networks, achieving higher accuracy in classification than DeepWalk described in “DeepWalk Overview, Algorithms, and Example Implementations,” and other methods.
GraphSAGE is known as a leading example of Spatial graph convolution because it can learn effective node embedding by combining more local and global information than other graph embedding algorithms such as DeepWalk, known as a baseline in graph neural network research.
The code for GraphSAGE by Hamilton et al. is available on the git page.
Specific procedures for GraphSAGE
The specific steps for GraphSAGE are as follows. This is the basic framework for learning to embed nodes and can be tailored to your application.
1. graph preparation:
Obtain or construct graph data. A graph consisting of nodes and edges (connections between nodes) is needed, which will be the data used in various applications such as social networks, web page link graphs, recommendation systems, etc.
2. sampling of adjacent nodes of a node:
Sampling adjacent nodes from around each node. This sampling is done to capture the local structural information of the node, and sampling methods may include random sampling, weighted sampling, and sampling of neighboring nodes.
3. aggregation:
Aggregate the sampled neighbor node information. Aggregation methods can include average pooling, maximum pooling, and attention mechanisms, whereby each node collects the information of its neighbors and updates its embedding.
4. neural network model design:
GraphSAGE uses a multi-layered neural network to learn the embedding. At each layer, sampling and aggregation alternate, and the output of each layer is used as input to the next layer. Typically, the output dimension and activation function of each layer are adjusted as hyperparameters.
5. training the model:
The neural network model is trained. The training data consists of sampled nodes and their neighbors, and the goal would be to learn embeddings and acquire embeddings suitable for the target task (e.g., class classification, link prediction).
6. obtaining embeddings:
Once training is complete, embeddings for each node are obtained. These embeddings are low-dimensional vector representations of the nodes and can be used for the target task.
7. use for application tasks:
Use the learned embeddings to solve a variety of graph data-related tasks. For example, they can be used for tasks such as node clustering, classification, link prediction, and recommendation.
Examples of GraphSAGE implementations
An example implementation of GraphSAGE is shown below. The following code example implements GraphSAGE using Python and PyTorch.
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import random
import numpy as np
import networkx as nx
from sklearn.preprocessing import OneHotEncoder
from sklearn.metrics import accuracy_score
# Read or generate graphs
G = nx.karate_club_graph()
# Randomly generated node features
node_features = {node: np.random.rand(5) for node in G.nodes()}
# Sampling Parameters
num_neighbors = 5 # Number of adjacent nodes
num_samples = 10 # Number of sampling times
num_epochs = 100
learning_rate = 0.01
# Generate class labels for nodes
labels = {node: 0 if G.nodes[node]['club'] == 'Mr. Hi' else 1 for node in G.nodes()}
# One-Hot encoding of class labels
labels = np.array(list(labels.values())).reshape(-1, 1)
encoder = OneHotEncoder(sparse=False)
labels_onehot = encoder.fit_transform(labels)
# Calculate the degree of a graph
degrees = dict(G.degree())
# Definition of the GraphSAGE model
class GraphSAGE(nn.Module):
def __init__(self, input_dim, hidden_dim, output_dim):
super(GraphSAGE, self).__init__()
self.fc1 = nn.Linear(input_dim, hidden_dim)
self.fc2 = nn.Linear(hidden_dim, output_dim)
def forward(self, node_features, sampled_neighbors):
aggregated = torch.mean(node_features[sampled_neighbors], dim=1)
x = F.relu(self.fc1(aggregated))
x = self.fc2(x)
return x
# Model initialization
input_dim = 5
hidden_dim = 16
output_dim = 2
model = GraphSAGE(input_dim, hidden_dim, output_dim)
# Setting up loss functions and optimization algorithms
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=learning_rate)
# training
for epoch in range(num_epochs):
loss_accumulated = 0.0
for node in G.nodes():
for _ in range(num_samples):
# Randomly sampled adjacent nodes
sampled_neighbors = random.sample(list(G.neighbors(node)), num_neighbors)
sampled_neighbors = torch.tensor(sampled_neighbors)
# forward pass
logits = model(torch.tensor(node_features[node], dtype=torch.float32),
sampled_neighbors)
# Loss Calculation
loss = criterion(logits.view(1, -1), torch.tensor([labels[node]], dtype=torch.long))
loss_accumulated += loss.item()
# back-propagation
optimizer.zero_grad()
loss.backward()
optimizer.step()
print(f"Epoch [{epoch+1}/{num_epochs}] Loss: {loss_accumulated}")
# inference
predicted_labels = []
true_labels = []
for node in G.nodes():
sampled_neighbors = list(G.neighbors(node))
logits = model(torch.tensor(node_features[node], dtype=torch.float32), sampled_neighbors)
predicted_label = torch.argmax(logits).item()
true_label = labels[node][0]
predicted_labels.append(predicted_label)
true_labels.append(true_label)
# Accuracy Rating
accuracy = accuracy_score(true_labels, predicted_labels)
print(f"Accuracy: {accuracy}")This code example uses a simple Karate Club graph: a GraphSAGE model is defined, the model is trained on a specified number of samplings and epochs, and the final classification accuracy is evaluated.
Challenge for GraphSAGE
GraphSAGE is an excellent graph embedding algorithm, but there are some challenges. These issues are described below.
1. Sampling Bias:
GraphSAGE samples neighboring nodes by random sampling or other methods, which may cause some nodes to be sampled frequently and others to be ignored, leading to unbalanced node embedding and poor performance.
2. node representativeness constraints:
GraphSAGE uses simple aggregation methods such as averages when aggregating information from neighboring nodes. This can limit the expressiveness of nodes, making it difficult to capture complex structures and features.
3. selection of adjacent nodes:
Sampling of adjacent nodes is important in GraphSAGE. There are several methods, including random sampling and weighted sampling, but the choice of which nodes to sample has a significant impact on the task, making it difficult to select an appropriate sampling method.
4. dealing with non-homogeneity of graphs:
While GraphSAGE is suitable for homogeneous graphs (where all edges are of the same type), it is not directly applicable to non-homogeneous graphs (where different edge types exist). To accommodate non-homogeneous graphs, the model needs to be extended.
5. hyperparameter tuning:
GraphSAGE has several hyperparameters (number of sampling, number of embedded dimensions, learning rate, etc.), which need to be tuned appropriately. The choice of hyperparameters varies from task to task and requires adjustment.
To address these issues, improved sampling methods, better aggregation methods, extensions to non-homogeneous graphs, and tuning of hyperparameters are being developed. Development of more advanced graph embedding algorithms and models is also underway, and it is important to tailor the selection to specific tasks and data.
Measures to Address GraphSAGE’s Challenges
The following countermeasures have been proposed to address GraphSAGE’s challenges
1. reduce sampling bias:
To reduce sampling bias, adopt smarter sampling methods instead of random sampling. For example, methods such as Metapath2Vec described in “Overview of Metapath2Vec and examples of algorithms and implementations” reduce bias by sampling based on specific paths, called metapaths.
2. improved aggregation methods:
More sophisticated aggregation methods can improve the representativeness of nodes. For example, the Attention Mechanism described in “Attention in Deep Learning” can be used to weight important neighboring nodes, and Convolutional Neural Networks (CNN) described in “Overview of CNN and examples of algorithms and implementations” can be applied.
3. use of multi-layer models:
More complex node representations can be learned by using a more multi-layered model. Multilayer models that alternate between graph sampling and aggregation contribute to the performance improvement of GraphSAGE.
4. extensions to non-homogeneous graphs:
There are ways to extend the model to deal with non-homogeneous graphs. For example, there are ways to define metapaths to handle different edge types of non-homogeneous graphs as described in “How to Define Metapaths to Handle Different Edge Types of Non-Homogeneous Graphs” or to use models such as R-GCN (Relational Graph Convolutional Networks (R-GCN) as described in “Overview of R-GCN and examples of algorithms and implementations“.
5. real-time training and incremental training:
If the graph changes dynamically, it is necessary to adapt the embedding to the latest information using real-time or incremental training.
6. hyper-parameter tuning:
Proper tuning of hyperparameters contributes to the performance improvement of GraphSAGE. It is important to find the optimal hyperparameters using methods such as cross-validation.
7. evaluation on diverse datasets:
Since graph datasets have different properties, it is important to evaluate the model on a variety of datasets to confirm its generality.
Reference Information and Reference Books
For more information on graph data, see “Graph Data Processing Algorithms and Applications to Machine Learning/Artificial Intelligence Tasks. Also see “Knowledge Information Processing Techniques” for details specific to knowledge graphs. For more information on deep learning in general, see “About Deep Learning.
Reference book is
“Graph Neural Networks: Foundations, Frontiers, and Applications“等がある。
“Introduction to Graph Neural Networks“
“Graph Neural Networks in Action“
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