Basic  

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. In graph, the Cosine Similairity algorithm uses N node properties to represent node as vector, and applies to two nodes.

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

Basic Concept

Vectorial Angle

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:

Vectorial Angle in Graph

When comparing two nodes in graph, two vectors are established by N specified numeric properties, and vectorial angle can be calculated according to the following formula:

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 and run the Cosine Similarity algorithm:

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

Algorithm statistics: N/A

Command and Configuration

• Command: algo(cosine_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(cosine_similarity).params({
  uuids: [1,2],
  uuids2: [3,4],
  node_schema_property: [price, weight]
}) as cs
return cs

Algorithm Execution

Task Writeback

1. File Writeback

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

algo(cosine_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 of node UUID = 1 and other nodes through properties price, weight, width and height, define algorithm results as alias named cs and return the results

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

Streaming Return

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

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

Real-time Statistics

This algorithm has no statistics.