Graph Embedding Overview
Graph Embedding (Graph Embedding) is a combined graph theory and machine learning approach that maps the graph structure into a low-dimensional vector space, representing the nodes and edges of the graph as dense numerical vectors, which are then processed by a machine learning algorithm.
The purpose of graph embedding is to represent each node as a dense vector while preserving information about the graph structure, and this representation makes it possible to handle a wide variety of information. In addition, the distance between nodes, which is conventionally represented by edges, can now be represented as a vector distance, which reduces the computational cost and can be used for tasks such as node classification, node clustering, graph visualization, and link prediction, by applying parallel and distributed algorithms. Their applications are summarized in “A Survey on Network Embedding“.
The advantage of node embedding is that it allows learning by vectorizing structural information over many node attributes, facilitating the application of deep learning algorithms. Tasks for which node embedding can be applied include dimensional compression of structural information that takes into account node attribute information, which has been difficult to achieve with the conventional graph data approach. Typical graph embedding methods include DeepWalk、LINE、node2Vec、GraRep、GCN、GraphSAGE、Variational Graph AutoEncoder.
Algorithm for graph embedding
Typical graph embedding algorithms are described below.
1. DeepWalk:
Idea: DeepWalk uses a random walk in the graph to generate a sequence of nodes, which is processed in a Word2Vec-like fashion to learn the representation of the nodes. For more information on random walks, see “Overview of Random Walks, Algorithms, and Examples of Implementations.
Procedure:
1. Generate a sequence of nodes by random walk, moving randomly in the graph.
2. Based on the generated sequence, learn the vector representation of each node using a method such as Word2Vec.
3. learn to predict the context around a node using the CBOW (Continuous Bag of Words) or Skip-gram model of Word2Vec.
Feature: Through random walks, a representation of the node is obtained that takes into account both the local and global structure of the graph.
For more information on DeepWalk, please refer to “DeepWalk Overview, Algorithm and Example Implementation.
2. Node2Vec:
Idea: Node2Vec learns a representation of a node based on a random walk, but by controlling the parameters of the random walk, different representations can be obtained.
Procedure:
1. generate a sequence of visits to each node’s neighbors using a random walk
2. mimic different search strategies such as depth-first search (DFS) or breadth-first search (BFS) by setting the transition probabilities of the random walk
3. learn a vector representation of each node based on the generated sequence using a Word2Vec-like method.
Features: by changing the parameters of the random walk, it is possible to focus on local or global structures.
For more details on Node2Vec, please refer to “Node2Vec Overview, Algorithm, and Example Implementation.
3. GraphSAGE (Graph Sample and Aggregated):
Idea: GraphSAGE learns the representation of a node by aggregating the neighborhood information of the nodes using techniques such as those described in “Overview of Message Passing in Machine Learning with Examples of Algorithms and Implementations“. This avoids using information from the entire graph and improves scalability.
Procedure:
1. For each node, collect features from its neighbors.
2. Aggregate the collected features using functions such as average and maximum to generate a new representation of the node.
3. By repeating this process hierarchically, the representation of each node is learned while taking into account more global information.
Feature: Since the representation of each node is updated through the aggregation of neighborhood information, a representation that takes into account both local and global structure is obtained.
For details of GraphSAGE, please refer to “GraphSAGE Overview, Algorithm, and Example Implementation“.
4. Graph Attention Networks (GAT):
Idea: GAT is an approach that learns the representation of nodes using the attention mechanism described in “Attention in Deep Learning,” weights the relationships between nodes, and focuses on the more important nodes.
Procedure:
1. For each node, collect information from its neighbors.
2. using the attention mechanism, compute weights between each node, thereby giving more weight to important neighbors.
3. Compute a new representation of each node using the weighted information.
Feature: The attention mechanism allows each node to learn which other nodes to pay attention to and update its representation.
For more information on GAT, see also “Overview of GAT (Graph Attention Network), Algorithm and Example Implementation.
Application Examples of Graph Embedding
Graph Embedding is widely used in various fields. The following are examples of such applications.
1. social network analysis:
Friend recommendation: Friend recommendation in social networks is done using graph embedding. New friends are recommended based on node (user) characteristics and connectivity.
Community detection: embedding representations of nodes to perform similarity and clustering when discovering communities within a social network. For example, people with the same interests and concerns can be grouped into the same community.
2. recommender system:
Product recommendation: Graph embedding is used to represent relationships between products and users and to recommend the best products for individual users, using vector representations of similar users and products.
3. information retrieval and similarity:
Document Similarity: To understand similarities between documents, documents are converted into vector representations of words or topics and graph embedding is used. This helps in retrieving similar documents.
4. bioinformatics:
Protein Interactions: Graph embedding is used to represent proteins in protein interaction networks. This helps in understanding the interaction patterns of proteins considering their structure and function.
5. node classification and anomaly detection:
Graph Classification: Graph embedding is used to label and classify nodes. For example, user attributes may be represented in a graph, and users may be classified based on those attributes.
Anomaly Detection: Graph embedding is used to detect anomalous behavior or patterns in a graph. For example, it is used to detect unauthorized network traffic and abnormal user behavior.
6. Linguistic and Natural Language Processing:
Word Semantic Representation: Graph embedding is also used as a means to understand word semantics, allowing the co-occurrence relations of words to be represented in a graph and the graph embedding to be used to learn vector representations of words.
Examples of Graph Embedding Implementations
Graph Embedding can be implemented using various libraries and frameworks. These are described below.
1. implementation of DeepWalk
Library: gensim (Python library)
from gensim.models import Word2Vec
from gensim.models import DeepWalk
# DeepWalk models are learned based on graphs
model = DeepWalk(graph, walk_length=10, num_walks=80, workers=4)
model.train(window_size=5, iter=3)
# Obtain a vector representation of a node
node_embeddings = model.wv2. implementation of Node2Vec
Library: stellargraph (Python library)
from stellargraph import StellarGraph
from stellargraph.data import BiasedRandomWalk
from stellargraph import Node2Vec
# Load graphs into StellarGraph
G = StellarGraph(graph)
# Define Biased Random Walk
rw = BiasedRandomWalk(G)
# Learning Node2Vec model
model = Node2Vec(G, walk_length=10, num_walks=80, workers=4)
model.train(window_size=5, iter=3)
# Obtain a vector representation of a node
node_embeddings = model.wv3. implementation of GraphSAGE
Library: stellargraph (Python library)
from stellargraph import StellarGraph
from stellargraph.mapper import GraphSAGENodeGenerator
from stellargraph.layer import GraphSAGE
# Load graphs into StellarGraph
G = StellarGraph(graph)
# Define GraphSAGENodeGenerator
generator = GraphSAGENodeGenerator(G, batch_size=50, num_samples=[10, 5])
# Build GraphSAGE model
model = GraphSAGE(
layer_sizes=[128, 128], generator=generator, bias=True, dropout=0.5
)
x_inp, x_out = model.in_out_tensors()
# Compile Model
model.compile(optimizer="adam", loss="sparse_categorical_crossentropy", metrics=["acc"])
# Learning model
history = model.fit(generator.flow(train_node_ids, train_node_labels, shuffle=True), epochs=5)
# Obtain a vector representation of a node
node_embeddings = model.predict(generator.flow(G.nodes()))4. implementation of Graph Attention Networks (GAT)
Library: stellargraph (Python library)
from stellargraph import StellarGraph
from stellargraph.mapper import FullBatchNodeGenerator
from stellargraph.layer import GAT
# Load graphs into StellarGraph
G = StellarGraph(graph)
# Define FullBatchNodeGenerator
generator = FullBatchNodeGenerator(G, method="gat")
# Building the GAT model
model = GAT(
layer_sizes=[8, 8], activations=["elu", "elu"], generator=generator, bias=True, in_dropout=0.5, attn_heads=8, dropout=0.5, normalize="l2"
)
x_inp, predictions = model.in_out_tensors()
# Compile Model
model.compile(optimizer="adam", loss="sparse_categorical_crossentropy", metrics=["acc"])
# Learning model
history = model.fit(generator.flow(train_node_ids, train_node_labels), epochs=5)
# Obtain a vector representation of a node
node_embeddings = model.predict(generator.flow(G.nodes()))These will be simple implementation examples using the common Python libraries gensim and stellargraph.
Graph Embedding Issues and Measures to Address Them
Graph Embedding is a powerful tool, but it has some challenges. These issues and their solutions are described below.
1. scalability:
Challenge: For large graphs, graph embedding takes time to compute and train.
Solution:
Sampling: Sampling a portion of the graph for computation can be used for large graphs.
Mini-batch processing: Use mini-batch to streamline training.
Distributed processing: use multiple machines or GPUs to parallelize computations to improve scalability.
2. understanding and representing the structure of graphs:
Challenge: The structure of graphs is complex, and it is sometimes difficult to find an appropriate representation.
Solution:
Select an appropriate embedding method: Select an appropriate graph embedding method according to the nature and features of the graph.
Design of features: Proper design of node and edge features can improve embedding performance.
3. hierarchy of nodes and sparsity of the graph:
Challenge: Nodes in a graph may have hierarchical relationships. They may also have sparse connectivity.
Solution:
Hierarchical embedding: Use a hierarchical graph embedding technique to obtain an embedding that reflects the hierarchical structure.
Sparse representation: Select an appropriate technique to deal with graph sparsity, such as approximating adjacency matrices or using convolution operations.
4. Domain Specific Issues:
Challenge: Graph embedding performance may be degraded in certain domains.
Solution:
Domain Adaptation: Improve performance by taking into account domain-specific features and structures.
Transfer Learning: Using embeddings that have already been learned in other domains and adapting them to the domain of interest can be an effective approach.
5. evaluation and comparison:
Challenge: It is sometimes difficult to evaluate and compare graph embedding methods.
Solution:
Evaluation metrics for graph embedding: compare using metrics that evaluate performance on tasks such as node similarity, clustering, classification, etc.
Benchmark dataset: Evaluate and compare method performance using a standard benchmark dataset.
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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