✓ File Writeback ✕ Property Writeback ✓ Direct Return ✓ Stream Return ✕ Stats

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:

This algorithm has two calculation modes:

1. Pairing: when ids/uuids and ids2/uuids2 are both configured, pairing nodes in the first group with nodes in the second group (Cartesian product) to compute pair-wise similarities.
2. Selection: when only ids/uuids is configured, for each node in the group, computing pair-wise similarities between it and all other nodes in the graph in order to select the most similar nodes, the returned top_list includes all nodes that have similarity > 0 with it 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

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

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;

Direct Return

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: p

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

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: p

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