Cosine Similarity

Overview

In cosine similarity, data objects in a dataset are treated as vectors, and it uses the cosine value of the angle between two vectors to indicate the similarity between them. In the graph, N numeric node properties (features) are specified to form N-dimensional vectors; two nodes are considered similar if their vectors are similar.

Cosine similarity ranges from -1 to 1, where 1 indicates that the two vectors point in the same direction, and -1 indicates they point in opposite directions.

Concepts

Cosine Similarity

In 2-dimensional space, the cosine similarity between vectors A = [a1, a2] and B = [b1, b2] is computed as:

In 3-dimensional space, the cosine similarity between vectors A = [a1, a2, a3] and B = [b1, b2, b3] is computed as:

The following diagram shows the relationship between vectors A and B in 2D and 3D spaces, as well as the angle θ between them:

Generalized to N-dimensional space, cosine similarity is computed as:

Considerations

• The calculation of cosine similarity between two nodes is independent of their connectivity in the graph.
• The value of cosine similarity is independent of the length of the vectors, but only the direction of the vectors.

Example Graph

GQL
INSERT (:product {_id: "product1", price: 50, weight: 160, width: 20, height: 152}),
       (:product {_id: "product2", price: 42, weight: 90, width: 30, height: 90}),
       (:product {_id: "product3", price: 24, weight: 50, width: 55, height: 70}),
       (:product {_id: "product4", price: 38, weight: 20, width: 32, height: 66})

Parameters

Supports three computation modes:

• All-pairs: When both ids and ids2 are empty, computes similarity between all node pairs in the graph.
• Pairing: When both ids and ids2 are specified, computes similarity between each node in ids and each node in ids2.
• Selection: When only ids is specified (no ids2), computes similarity between each node in ids and all other nodes. Use top_limit to limit results per source node.

Run Mode

Returns:

Cosine similarity in pairing mode:

GQL
CALL algo.similarity({
  type: "cosine",
  ids: ["product1"],
  ids2: ["product2", "product3", "product4"],
  node_property: ["price", "weight", "width", "height"]
}) YIELD node1, node2, similarity

Result:

Cosine similarity in selection mode (top 1 per source node):

GQL
CALL algo.similarity({
  type: "cosine",
  ids: ["product1", "product3"],
  node_property: ["price", "weight", "width", "height"],
  top_limit: 1
}) YIELD node1, node2, similarity

Result:

Stream Mode

Returns the same columns as run mode, streamed for memory efficiency.

GQL
CALL algo.similarity.stream({
  type: "cosine",
  ids: ["product1"],
  node_property: ["price", "weight", "width", "height"],
  order: "desc"
}) YIELD node1, node2, similarity
RETURN node1, node2, similarity

Result:

Stats Mode

Returns:

GQL
CALL algo.similarity.stats({
  type: "cosine",
  node_property: ["price", "weight", "width", "height"]
}) YIELD pairCount, minSimilarity, maxSimilarity, avgSimilarity

Result:

Write Mode

Computes results and writes them back to node properties. The write configuration is passed as a second argument map.

Write parameters:

Writable columns:

Returns:

GQL
CALL algo.similarity.write({
  type: "cosine",
  ids: ["product1", "product2"],
  node_property: ["price", "weight", "width", "height"]
}, {
  db: {
    property: "sim_score"
  }
}) YIELD task_id, nodesWritten, computeTimeMs, writeTimeMs