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      Pearson Correlation Coefficient

      ✓ 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, ..., xn) and Y = (y1, y2, ..., yn) , 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:

      Pearson correlation coefficient
      Correlation type
      Interpretation
      0 < r ≤ 1 Positive correlation As one variable becomes larger, the other variable becomes larger
      r = 0 No linear correlation (May exist some other types of correlation)
      -1 ≤ r < 0 Negative correlation As one variable becomes larger, the other variable becomes smaller

      Considerations

      • Theoretically, the calculation of Pearson correlation coefficient between two nodes does not depend on their connectivity.

      Syntax

      • Command: algo(similarity)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      ids / uuids []_id / []_uuid / / No ID/UUID of the first group of nodes to calculate
      ids2 / uuids2 []_id / []_uuid / / Yes ID/UUID of the second group of nodes to calculate
      type string pearson cosine No Type of similarity; for Pearson Correlation Coefficient, keep it as pearson
      node_schema_property []@<schema>?.<property> Numeric type, must LTE / No Specify two or more node properties to form the vectors, all properties must belong to the same (one) schema
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results
      top_limit int ≥-1 -1 Yes In the selection mode, limit the maximum number of results returned for each node specified in ids/uuids, -1 to return all results with similarity > 0; in the pairing mode, this parameter is invalid

      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

      Spec Content
      filename node1,node2,similarity
      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
      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

      Alias Ordinal
      Type
      Description Columns
      0 []perNodePair Node pair and its similarity node1, node2, similarity
      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

      node1 node2 similarity
      1 2 0.998785121601255
      1 3 0.474383803132863
      1 4 0.210494150169583
      2 3 0.50783775659896
      2 4 0.253573071269506
      algo(similarity).params({
        uuids: [1,2],
        type: 'pearson',
        node_schema_property: ['price', 'weight', 'width', 'height'],
        top_limit: 1
      }) as top
      return top
      

      Results: top

      node1 node2 similarity
      1 2 0.998785121601255
      2 1 0.998785121601255

      Stream Return

      Alias Ordinal
      Type
      Description Columns
      0 []perNodePair Node pair and its similarity node1, node2, similarity
      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

      node1 node2 similarity
      3 1 0.167101674410905
      3 2 0.181677473801374
      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

      node1 node2 similarity
      1 2 0.998785121601255
      3 2 0.50783775659896
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