Transductive learning is useful when the graph you want to analyze is known and relatively stable. A transductive embedding method learns a representation for each node in that fixed graph, using its structure during training. The resulting vectors can become inputs to classification, recommendation, or clustering tasks. section 2.4.2 section 2.1.4
Node2Vec (N2V) shows the workflow:
- Start with the graph’s nodes and edges. Their connections provide the context for learning, so check that the graph represents the relationships relevant to the task. section 2.1.4
- Simulate walks through the graph to capture which nodes occur near one another, then learn a dense vector for each node in the training graph. section 2.1.4 section 2.4.2
- Use those vectors as features for a downstream task. Because the method optimized representations for known nodes rather than learning a general embedding function, a new node cannot naturally receive an embedding without retraining. section 2.1.4 section 2.4.2
Choosing between a fixed and a changing graph
In a political-books co-purchase graph, N2V embeddings could help predict a known book’s political leaning or recommend related books. For community detection in a social network, a transductive method can exploit the available graph, including labeled and unlabeled nodes. Incoming-email spam detection is a poor fit: retraining for each new batch would be impractical. section 2.1.4 section 2.4.2
The trade-off is specificity versus adaptability. Access to the complete, stable graph lets transductive methods capture detailed relationships, and random-walk methods can work from graph structure without additional node features. But they are costly at large scale and do not naturally extend to unseen nodes or graphs. Inductive methods such as GraphSAGE and other graph neural networks instead learn from features and local structure to generate embeddings for new data. N2V extensions can also support inductive settings, so the distinction describes the method’s learning approach, not an absolute limit on every variant. section 2.1.4 section 2.4.2 section 2.2
Table 2.5 Different methods of graph representation
|
Representation
|
Description
|
Examples
|
|---|---|---|
|
Basic data representations
|
• Great for analytical methods that involve network traversal
• Useful for some node classification algorithms
• Information provided: Node and edge neighbors
|
• Adjacency list
• Edge list
• Adjacency matrix
|
|
Transductive (shallow) embeddings
|
• Useless for data not trained on
• Difficult to scale
|
• DeepWalk
• N2V
• TransE
• RESCAL
• Graph factorization
• Spectral techniques
|
|
Inductive embeddings
|
• Models can be generalized to new and structurally different graphs
• Represents data as vectors in continuous space
• Learns a mapping from data (new and old) to positions within the continuous space
|
• GNNs can be used to inductively generate embeddings
• Transformers
• N2V with feature concatenation
|
Compare transductive embeddings with basic graph representations and inductive embeddings when deciding whether unseen data and scaling matter. section 2.4.2
