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.

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

• Theoretically, 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

Run the following statements on an empty graph to define its structure and insert data:

GQLUQL
ALTER GRAPH CURRENT_GRAPH ADD NODE {
  product ({price int32, weight int32, width int32, height int32})
};
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});

Creating HDC Graph

To load the entire graph to the HDC server hdc-server-1 as my_hdc_graph:

GQLUQL
CREATE HDC GRAPH my_hdc_graph ON "hdc-server-1" OPTIONS {
  nodes: {"*": ["*"]},
  edges: {"*": ["*"]},
  direction: "undirected",
  load_id: true,
  update: "static"
}

Parameters

Algorithm name: similarity

File Writeback

GQLUQL
CALL algo.similarity.write("my_hdc_graph", {
  return_id_uuid: "id",
  ids: "product1",
  ids2: ["product2", "product3", "product4"],
  node_schema_property: ["price", "weight", "width", "height"],
  type: "cosine"
}, {
  file: {
    filename: "cosine"
  }
})

Result:

File: cosine
_id1,_id2,similarity
product1,product2,0.986529
product1,product3,0.878858
product1,product4,0.816876

Full Return

GQLUQL
CALL algo.similarity.run("my_hdc_graph", {
  return_id_uuid: "id",
  ids: ["product1","product2"], 
  ids2: ["product2","product3","product4"],
  node_schema_property: ["price", "weight", "width", "height"],
  type: "cosine"
}) YIELD cs
RETURN cs

Result:

Stream Return

GQLUQL
CALL algo.similarity.stream("my_hdc_graph", {
  return_id_uuid: "id",
  ids: ["product1", "product3"], 
  node_schema_property: ["price", "weight", "width", "height"],
  type: "cosine",
  top_limit: 1    
}) YIELD top
RETURN top

Result: