Overview

Cosine similarity uses the cosine value of the angle formed by two N-dimensional vectors in vector space to indicate the similarity between them. Cosine similarity between two nodes in graph is calculated by using N properties of node to form two N-dimensional vectors.

The range of cosine similarity values is [0,1]; the larger the value, the more similar the two nodes are.

Basic Concept

Vector

Vector is one of the basic concepts in Advanced Mathematics, vectors in low dimensional spaces are relatively easy to understand and express. The following diagram shows the relationship between vectors A, B and coordinate axes in 2- and 3-dimensional spaces respectively, as well as the angle θ between them:

When comparing two nodes in graph, N properties of node are used to form the two N-dimensional vectors.

Cosine Similarity

In 2-dimensional space, the formula to calculate the cosine similarity is:

In 3-dimensional space, the formula to calculate the cosine similarity is:

Generalize to n-dimensional space, the formula to calculate the cosine similarity is:

Special Case

Lonely Node, Disconnected Graph

Theoretically, the calculation of cosine similarity between two nodes does not depend on the existence of edges in the graph. Regardless of whether the two nodes to be calculated are lonely nodes or whether they are in the same connected component, it does not affect the calculation of their cosine similarity.

Self-loop Edge

The calculation of cosine similarity has nothing to do with edges.

Directed Edge

The calculation of cosine similarity has nothing to do with edges.

Results and Statistics

The graph below has 4 product nodes (edges are ignored), use properties price, weight, weight and height to form vector:

Algorithm results: Calculate cosine similarity between product1 and other 3 products, return node1, node2 and similarity

Algorithm statistics: N/A

Command and Configuration

• Command: algo(similarity)
• Configurations for the parameter params():

Example: Calculate cosine similarity of nodes UUID = 1,2 and nodes UUID = 3,4 through properties price and weight

algo(similarity).params({
  uuids: [1,2],
  uuids2: [3,4],
  node_schema_property: [price, weight],
  type: "cosine"
}) as p
return p

Algorithm Execution

Task Writeback

1. File Writeback

Example: Calculate cosine similarity between node UUID = 1 and other nodes through properties price, weight, width and height, write the algorithm results back to file named cs_result

algo(similarity).params({
  uuids: [1], 
  uuids2: [2,3,4],
  node_schema_property: [price,weight,width,height]
}).write({
  file:{ 
    filename: "cs_result"
  }
})

2. Property Writeback

Not supported by this algorithm.

3. Statistics Writeback

This algorithm has no statistics.

Direct Return

Example: Calculate cosine similarity between node UUID = 1 and other nodes through properties price, weight, width and height, define algorithm results as alias named similarity and return the results

algo(similarity).params({
  uuids: [1], 
  uuids2: [2,3,4],
  node_schema_property: [price,weight,width,height],
  type: "cosine"
}) as similarity 
return similarity

Streaming Return

Example: Calculate cosine similarity between node UUID = 1 and other nodes through properties price, weight, width and height, define algorithm results as alias named similarity, return 2 results

algo(similarity).params({
  uuids: [1], 
  uuids2: [2,3,4],
  node_schema_property: [price,weight,width,height],
  type: "cosine"
}).stream() as similarity 
return similarity limit 2

Real-time Statistics

This algorithm has no statistics.