node2vec
The node2vec is a semi-supervised algorithmic framework for learning continuous feature representations for nodes in networks. The algorithm generates a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. By using a biased random walk procedure, it enables exploring diverse neighborhoods. In tasks such as multi-label classification and link prediction, node2vec shows great results. Check out Scalable Feature Learning for Networks (opens in a new tab) by A. Grover and J. Leskovec.
The node2vec algorithm was inspired by a similar NLP technique. The same way as a document is an ordered sequence of words, by sampling sequences of nodes from the underlying network and turning a network into an ordered sequence of nodes. Although the idea of sampling is easy, choosing the actual strategy can be challenging and dependant on the techniques that will be applied afterward.
Capturing information in networks often shuttles between two kinds of similarities: homophily and structural equivalence. Under the homophily hypothesis, nodes that are highly interconnected and belong to similar network clusters or communities should be embedded closely together. In contrast, under the structural equivalence hypothesis, nodes that have similar structural roles in networks should be embedded closely together (e.g., nodes that act as hubs of their corresponding communities).
The current implementation easily captures homophily or structural equivalence by changing hyperparameters.
BFS
and DFS
strategies play a key role in producing representations that
reflect either of the above equivalences. The neighborhoods sampled by BFS
lead to embeddings that correspond closely to structural equivalence. The
opposite is true for DFS
. It can explore larger parts of the network as it
can move further away from the source node. Therefore, DFS
sampled walks
accurately reflect a macro-view of the neighborhood, which is essential in
inferring communities based on homophily.
By having different parameters:
- return parameter
p
- and in-out parameter
q
one decides whether to prioritize the BFS
or DFS
strategy when sampling. If
p
is smaller than 1, then we create more BFS
like walks and we capture more
structural equivalence. The opposite is true if q
is smaller than 1. Then we
capture DFS
like walks and homophily.
node2vec can be used for link prediction (opens in a new tab). We recommend you use the link prediction with GNN as it's more precise (node2vec gives a correct results in approximately 35% cases, while GNNs are correct in approximately 75% cases).
Trait | Value |
---|---|
Module type | module |
Implementation | Python |
Graph direction | directed/undirected |
Edge weights | weighted/unweighted |
Parallelism | sequential |
Too slow?
If this algorithm implementation is too slow for your use case, open an issue on Memgraph's GitHub repository (opens in a new tab) and request a rewrite to C++!
Procedures
You can execute this algorithm on graph projections, subgraphs or portions of the graph.
get_embeddings()
The procedure returns calculated embeddings and the corresponding list of embeddings.
Input:
subgraph: Graph
(OPTIONAL) ➡ A specific subgraph, which is an object of type Graph returned by theproject()
function, on which the algorithm is run.is_directed : boolean
➡ IfTrue
, graph is treated as directed, otherwise it's treated as undirectedp : float
➡ Return hyperparameter for calculating transition probabilities.q : float
➡ In-out hyperparameter for calculating transition probabilities.num_walks : integer
➡ The number of walks per node in the walk sampling.walk_length : integer
➡ Length of one walk in the walk sampling.vector_size : integer
➡ Dimensionality of the word vectors.alpha : float (default=0.025)
➡ The initial learning rate.window : integer
➡ The maximum distance between the current and predicted word within a sentence.min_count : integer
➡ Ignores all words with total frequency lower than this.seed : integer
➡ Seed for the random number generator. Initial vectors for each word are seeded with a hash of the concatenation of word +str(seed)
.workers : integer
➡ Use these many worker threads to train the model (=faster training with multicore machines).min_alpha : float
➡ Learning rate will linearly drop tomin_alpha
as training progresses.sg : {0, 1}
➡ Training algorithm: 1 for skip-gram; otherwise CBOW.hs : {0, 1}
➡ If 1, hierarchical softmax will be used for model training. If 0, andnegative
is > 0, negative sampling will be used.negative : integer
➡ If > 0, negative sampling will be used, the integer for negative specifies how many "noise words" should be drawn (usually between 5-20). If set to 0, no negative sampling is used. Eithernegative
must be > 0 orhs
must be set to 1.epochs : integer (default=5)
edge_weight_property : string (default="weight")
Output:
nodes: mgp.List[mgp.Vertex]
➡ List of nodes for which embeddings were calculatedembeddings: mgp.List[mgp.List[mgp.Number]]
➡ Corresponding list of embeddings
Usage:
To get the calculated embeddings and the corresponding list of embeddings, use the following query:
CALL node2vec.get_embeddings(False, 2.0, 0.5, 4, 5, 100, 0.025, 5, 1, 1, 1, 0.0001, 1, 0, 5, 5, "weight");
set_embeddings()
The procedure calculates embeddings, creates a property of type List
on a node
with the embedding values and returns the corresponding list of embeddings.
Input:
subgraph: Graph
(OPTIONAL) ➡ A specific subgraph, which is an object of type Graph returned by theproject()
function, on which the algorithm is run.is_directed : boolean
➡ IfTrue
, graph is treated as directed, else not directedp : float
➡ Return hyperparameter for calculating transition probabilities.q : float
➡ In-out hyperparameter for calculating transition probabilities.num_walks : integer
➡ The number of walks per node in walk sampling.walk_length : integer
➡ Length of one walk in walk sampling.vector_size : integer
➡ Dimensionality of the word vectors.alpha : float
➡ The initial learning rate.window : integer
➡ The maximum distance between the current and predicted word within a sentence.min_count : integer
➡ Ignores all words with total frequency lower than this.seed : integer
➡ Seed for the random number generator. Initial vectors for each word are seeded with a hash of the concatenation of word +str(seed)
.workers : integer
➡ Use these many worker threads to train the model (=faster training with multicore machines).min_alpha : float
➡ Learning rate will linearly drop tomin_alpha
as training progresses.sg : {0, 1}
➡ Training algorithm: 1 for skip-gram; otherwise CBOW.hs : {0, 1}
➡ If 1, hierarchical softmax will be used for model training. If 0, andnegative
is non-zero, negative sampling will be used.negative : integer
➡ If > 0, negative sampling will be used, the int for negative specifies how many "noise words" should be drawn (usually between 5-20). If set to 0, no negative sampling is used.epochs : integer (default=5)
edge_weight_property : string (default="weight")
Output:
nodes: mgp.List[mgp.Vertex]
➡ List of nodes for which embeddings were calculatedembeddings: mgp.List[mgp.List[mgp.Number]]
➡ Corresponding list of embeddings
Usage:
To calculate embeddings, use the following query:
CALL node2vec.set_embeddings(False, 2.0, 0.5, 4, 5, 100, 0.025, 5, 1, 1, 1, 0.0001, 1, 0, 5, 5, "weight");
help()
The procedure returns the list of available procedures and input parameters.
Output:
name: string
➡ Names of the available functions.value: string
➡ Documentation for every function.
Usage:
To get help about the queries from this module, use the following query:
CALL node2vec.help()
YIELD name, value
RETURN name, value;
Example
Database state
The database contains the following data:
Created with the following Cypher queries:
MERGE (n:Node {id: 1}) MERGE (m:Node {id: 6}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 2}) MERGE (m:Node {id: 6}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 10}) MERGE (m:Node {id: 5}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 5}) MERGE (m:Node {id: 2}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 9}) MERGE (m:Node {id: 7}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 7}) MERGE (m:Node {id: 3}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 3}) MERGE (m:Node {id: 6}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 9}) MERGE (m:Node {id: 8}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 8}) MERGE (m:Node {id: 4}) CREATE (n)-[:RELATION]->(m);
MERGE (n:Node {id: 4}) MERGE (m:Node {id: 6}) CREATE (n)-[:RELATION]->(m);
Set embeddings
Use the following query to set a new node property with the calculated embeddings:
CALL node2vec.set_embeddings(False, 2.0, 0.5, 4, 5, 2)
YIELD nodes, embeddings
RETURN nodes, embeddings;
Check embeddings
Run the following query to check the embeddings:
MATCH (n)
RETURN n.id as node, n.embedding as embedding
ORDER BY n.id;
Result:
+-------------------------+-------------------------+
| node | embedding |
+-------------------------+-------------------------+
| 1 | [-0.243723, -0.0916009] |
| 2 | [0.25442, 0.449585] |
| 3 | [0.322331, 0.448404] |
| 4 | [0.143389, 0.0492275] |
| 5 | [-0.465552, -0.35653] |
| 6 | [-0.0272922, 0.0111898] |
| 7 | [0.368725, -0.0773199] |
| 8 | [-0.414683, -0.472285] |
| 9 | [-0.226683, 0.328159] |
| 10 | [-0.251244, -0.189218] |
+-------------------------+-------------------------+