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    English

      Jaccard Similarity

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

      Overview

      Jaccard similarity, or Jaccard index, was proposed by Paul Jaccard in 1901. It’s a metric of similarity for two sets of data. In the graph, collecting the neighbors of a node into a set, two nodes are considered similar if their neighbor sets are similar.

      Jaccard similarity ranges from 0 to 1; 1 means that two sets are exactly the same, 0 means that the two sets do not have any element in common.

      Concepts

      Jaccard Similarity

      Given two sets A and B, the Jaccard similarity between them is computed as:

      In the following example, set A = {b,c,e,f,g}, set B = {a,d,b,g}, their intersection A⋂B = {b,g}, their union A⋃B = {a,b,c,d,e,f,g}, hence the Jaccard similarity between A and B is 2 / 7 = 0.2857.

      Neighbor Set

      In Ultipa's Jaccard Similarity algorithm, the following points have to be noted when collecting the neighbor sets of two target nodes to compute their similarity:

      • There is no repeated nodes in the neighbor set;
      • Self-loop is ignored;
      • Any edge between the two target nodes is ignored;
      • Edge direction is ignored.

      In the graph above, when computing the similarity between node u and node v, the neighbor sets for the two nodes are Nu = {a,b,c,d,e} and Nv = {d,e,f}, so their Jaccard similarity is 2 / 6 = 0.3333.

      In practice, you may need to convert some node properties into node schemas in order to calculate the similarity index that is based on common neighbors, just as the Jaccard Similarity. For instance, when considering the similarity between two applications, information like phone number, email, device IP, etc. of the application might have been stored as properties of @application node schema; they need to be designed as nodes and incorporated into the graph in order to be used for comparison.

      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 jaccard cosine No Type of similarity; for Jaccard Similarity, keep it as jaccard
      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 is as follows:

      File Writeback

      Spec Content
      filename node1,node2,similarity
      algo(similarity).params({
        ids: 'userC',
        ids2: ['userA', 'userB', 'userD'],
        type: 'jaccard'
      }).write({
        file:{ 
          filename: 'sc'
        }
      })
      

      Results: File sc

      userC,userA,0.25
      userC,userB,0.5
      userC,userD,0
      
      algo(similarity).params({
        uuids: [1,2,3,4],
        type: 'jaccard'
      }).write({
        file:{ 
          filename: 'list'
        }
      })
      

      Results: File list

      userA,userC,0.25
      userA,userB,0.2
      userA,userD:0.166667
      userB,userC:0.5
      userB,userD,0.25
      userB,userA,0.2
      userC,userB,0.5
      userC,userA,0.25
      userD,userB:0.25
      userD,userA:0.166667
      

      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],
        type: 'jaccard'
      }) as jacc
      return jacc
      

      Results: jacc

      node1 node2 similarity
      1 2 0.2
      1 3 0.25
      1 4 0.166666666666667
      2 3 0.5
      2 4 0.25
      algo(similarity).params({
        uuids: [1,2],
        type: 'jaccard',
        top_limit: 1
      }) as top
      return top
      

      Results: top

      node1 node2 similarity
      1 3 0.25
      2 3 0.5

      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],
        type: 'jaccard'
      }).stream() as jacc
      where jacc.similarity > 0
      return jacc
      

      Results: jacc

      node1 node2 similarity
      3 1 0.25
      3 2 0.5
      algo(similarity).params({
        uuids: [1],
        type: 'jaccard',
        top_limit: 2
      }).stream() as top
      return top
      

      Results: top

      node1 node2 similarity
      1 3 0.25
      1 2 0.2
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