Pearson Correlation Coefficient

Overview

The Pearson correlation coefficient is the most common way of measuring the strength and direction of the linear relationship between two quantitative variables. In the graph, nodes are quantified by N numeric properties (features) of them.

For two variables X= (x₁, x₂, ..., x_n) and Y = (y₁, y₂, ..., y_n) , Pearson correlation coefficient (r) is defined as the ratio of the covariance of them to the product of their standard deviations:

The Pearson correlation coefficient ranges from -1 to 1:

Considerations

• Theoretically, the calculation of Pearson correlation coefficient between two nodes is independent of their connectivity.

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: "pearson"
}, {
  file: {
    filename: "pearson"
  }
})

Result:

File: pearson
_id1,_id2,similarity
product1,product2,0.998785
product1,product3,0.474384
product1,product4,0.210494

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: "pearson"
}) YIELD p
RETURN p

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: "pearson",
  top_limit: 1    
}) YIELD top
RETURN top

Result: