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      Euclidean Distance

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

      Overview

      In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. In the graph, specifying N numeric properties (features) of nodes to indicate the location of the node in an N-dimensional Euclidean space.

      Concepts

      Euclidean Distance

      In 2-dimensional space, the formula to compute the Euclidean distance between points A(x1, y1) and B(x2, y2) is:

      In 3-dimensional space, the formula to compute the Euclidean distance between points A(x1, y1, z1) and B(x2, y2, z2) is:

      Generalize to N-dimensional space, the formula to compute the Euclidean distance is:

      where xi1 represents the i-th dimensional coordinates of the first point, xi2 represents the i-th dimensional coordinates of the second point.

      The Euclidean distance ranges from 0 to +∞; the smaller the value, the more similar the two nodes.

      Normalized Euclidean Distance

      Normalized Euclidean distance scales the Euclidean distance into range from 0 to 1; the closer to 1, the more similar the two nodes.

      Ultipa adopts the following formula to normalize the Euclidean distance:

      Considerations

      • Theoretically, the calculation of Euclidean distance 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 euclideanDistance, euclidean cosine No Type of similarity; euclideanDistance is to compute Euclidean Distance, euclidean is to compute Normalized Euclidean Distance
      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: 'euclideanDistance'
      }).write({
        file:{ 
          filename: 'ed'
        }
      })
      

      Results: File ed

      product1,product2,94.3822
      product1,product3,143.962
      product1,product4,165.179
      
      algo(similarity).params({
        uuids: [1,2,3,4],
        node_schema_property: ['price', 'weight', 'width', 'height'],
        type: 'euclidean'
      }).write({
        file:{ 
          filename: 'ed_list'
        }
      })
      

      Results: File ed_list

      product1,product2,0.010484
      product1,product3,0.006898
      product1,product4,0.006018
      product2,product3,0.018082
      product2,product4,0.013309
      product2,product1,0.010484
      product3,product4,0.024091
      product3,product2,0.018082
      product3,product1,0.006898
      product4,product3,0.024091
      product4,product2,0.013309
      product4,product1,0.006018
      

      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: 'euclideanDistance'
      }) as distance
      return distance
      

      Results: distance

      node1 node2 similarity
      1 2 94.3822017119753
      1 3 143.96180048888
      1 4 165.178691119648
      2 3 54.3046959295419
      2 4 74.1350119714025
      algo(similarity).params({
        uuids: [1,2],
        type: 'euclidean',
        node_schema_property: ['price', 'weight', 'width', 'height'],
        top_limit: 1
      }) as top
      return top
      

      Results: top

      node1 node2 similarity
      1 2 0.0104841362649574
      2 3 0.0180816471945529

      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: 'euclidean'
      }).stream() as distance
      where distance.similarity > 0.01
      return distance
      

      Results: distance

      node1 node2 similarity
      3 2 0.0180816471945529
      3 4 0.0240910110982062
      algo(similarity).params({
        uuids: [1,3],
        node_schema_property: ['price', 'weight', 'width', 'height'],
        type: 'euclideanDistance',
        top_limit: 1
      }).stream() as top
      return top
      

      Results: top

      node1 node2 similarity
      1 4 165.178691119648
      3 1 143.96180048888
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