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 and 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 does not depend on their connectivity.

Syntax

• Command: algo(similarity)
• Parameters:

The algorithm has two calculation modes:

1. Pairing: when both ids/uuids and ids2/uuids2 are configured, pairing each node in ids/uuids with each node in ids2/uuids2 (ignore the same node) and computing pair-wise similarities.
2. Selection: when only ids/uuids is configured, for each target node in it, computing pair-wise similarities between it and all other nodes in the graph. The returned results include all or limited number of nodes that have similarity > 0 with the target node and is ordered by the descending similarity.

Examples

The example graph has 4 products (edges are ignored), each product has properties price, weight, weight and height:

File Writeback

UQL
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

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

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

Results: File list

File
product1,product2,0.998785
product1,product3,0.474384
product1,product4,0.210494
product2,product1,0.998785
product2,product3,0.507838
product2,product4,0.253573
product3,product2,0.507838
product3,product1,0.474384
product3,product4,0.474021
product4,product3,0.474021
product4,product2,0.253573
product4,product1,0.210494

Direct Return

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

Results: p

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

Results: top

Stream Return

UQL
algo(similarity).params({
  uuids: [3], 
  uuids2: [1,2,4],
  node_schema_property: ['@product.price', '@product.weight', '@product.width'],
  type: 'pearson'
}).stream() as p
where p.similarity > 0
return p

Results: p

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

Results: top