Overview

The Pearson correlation coefficient measures the linear correlation between two variables. The Pearson correlation coefficient between two nodes in graph is calculated by using N properties of node to form two N-dimensional vectors.

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.

Pearson Correlation Coefficient

The range of Pearson correlation coefficient values is [-1,1]; let r to denote the Pearson correlation coefficient, then:

• r > 0 indicates positive correlation, i.e. as one variable becomes larger, the other variable becomes larger;
• r < 0 indicates negative correlation, i.e. as one variable becomes larger, the other variable becomes smaller;
• r = 1 or r = -1 indicates that two variables can be described by a linear equation, i.e. them fall on the same line;
• r = 0 indicates that there is no linear correlation (but may exist some other correlations).

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 and the product of their standard deviations:

Special Case

Isolated Node, Disconnected Graph

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

Self-loop Edge

The calculation of Pearson Correlation Coefficient has nothing to do with edges.

Directed Edge

The calculation of Pearson Correlation Coefficient has nothing to do with edges.

Command and Configuration

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

Calculation Mode

This algorithm has two calculation modes:

1. Pairing mode: when two sets of valid nodes are configured, pair each node in the first set with each node in the second set (Cartesian product), similarities are calculated for all node pairs.
2. Selection mode: when only one set (the first) of valid nodes are configured, for each node in the set, calculate its similarities with all other nodes in the graph, return the results if the similarity > 0, order the results the descending similarity.

Examples

Example Graph

The example graph has product1, product2, product3 and product4 (UUIDs are 1, 2, 3 and 4 in order; edges are ignored), product node has properties price, weight, weight and height:

Task Writeback

1. File Writeback

Example: Calculate Pearson correlation coefficient between product UUID = 1 and products UUID = 2,3,4 through properties price, weight, width and height, write the algorithm results back to file

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

Results: File pearson

product1,product2,0.998785
product1,product3,0.474384
product1,product4,0.210494

Example: Calculate Pearson correlation coefficient between products UUID = 1,2,3,4 and all other products in the graph respectively through properties price, weight, width and height, write the algorithm results back to file

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

Results: File list

product1,product2:0.998785;product3:0.474384;product4:0.210494;
product2,product1:0.998785;product3:0.507838;product4:0.253573;
product3,product2:0.507838;product1:0.474384;product4:0.474021;
product4,product3:0.474021;product2:0.253573;product1:0.210494;

2. Property Writeback

Not supported by this algorithm.

3. Statistics Writeback

This algorithm has no statistics.

Direct Return

Example: Calculate Pearson correlation coefficient between product UUID = 1 and products UUID = 2,3,4 through properties price, weight, width and height, order results in the ascending similarity

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

Results:

Example: Select the product with the highest Pearson correlation coefficient with products UUID = 1,2 respectively through properties price, weight, width and height,

algo(similarity).params({
  uuids: [1,2],
  type: "pearson",
  node_schema_property: [price,weight,width,height],
  top_limit: 1
}) as top
return top

Results:

Streaming Return

Example: Calculate Pearson correlation coefficient between product UUID = 3 and products UUID = 1,2,4 through properties price, weight, width and height, only return results that have similariy above 0.5

algo(similarity).params({
  uuids: [3], 
  uuids2: [1,2,4],
  node_schema_property: [price,weight,width,height],
  type: "pearson"
}).stream() as p
where p.similarity > 0.5
return p

Results:

Example: Select the product with the highest Pearson correlation coefficient with products UUID = 1,3 respectively

algo(similarity).params({
  uuids: [1,3],
  node_schema_property: [price,weight,width,height],
  type: "pearson",
  top_limit: 1
}).stream() as top
return top

Results:

Real-time Statistics

This algorithm has no statistics.