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      kNN (k-Nearest Neighbors)

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

      Overview

      The k-Nearest Neighbors (kNN) algorithm is a classification technique that classifies the target node based on the classifications of its k nearest (most similar) nodes. kNN was proposed by T.M. Cover and P.E. Hart in 1967 and has since become one of the simplest and widely used classification algorithms:

      Although containing the word neighbor in its name, kNN does not explicitly consider the edges between nodes when calculating similarity. Instead, it focuses solely on node properties.

      Concepts

      Similarity Metric

      Ultipa's kNN algorithm computes pair-wise cosine similarity between the target node and all other nodes in the graph, then selects the k nodes with the highest similarity to the target node.

      Vote on Classification

      One node property is selected as the class label. After finding the nearest k nodes for the target node, assign the majority label among the k nodes to the target node.

      If multiple labels occur with the highest frequency, the label of the node with the highest similarity will be selected.

      Syntax

      • Command: algo(knn)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      node_id _uuid / / No UUID of the target node
      node_schema_property []@<schema>?.<property> Numeric type, must LTE, must be of the same schema as the target node / No Two or more node properties to compute the cosine similarity
      top_k int >0 / No The number of the nearest nodes to select
      target_schema_property @<schema>?.<property> Numeric/String type, must LTE, must be of the same schema as the target node / No Node property to use as the class label

      Examples

      The example graph has 6 image nodes (edges are ignored), and each node has properties d1, d2, d3, d4 and type:

      File Writeback

      Spec
      Content
      Description
      filename First row: attribute_value
      Second row and later: _id,similarity
      First row: The elected class label
      Second row and later: ID of the nearest node and its cosine similarity with the target node
      algo(knn).params({
        node_id: 1,
        node_schema_property: ['d1', 'd2', 'd3', 'd4'],
        top_k: 4,
        target_schema_property: @image.type
      }).write({
        file:{
          filename: "knn"
          }
      })
      

      Results: File knn

      Gold
      top k : image4,0.538975
      image3,0.705072
      image6,0.841922
      image2,0.85516
      

      Direct Return

      Alias Ordinal
      Type
      Description
      Columns
      0 KV The elected class label and its number of occurrences among the k nearest neighbors attribute_value, count
      1 []perNode The nearest node and its cosine similarity with the target node node, similarity
      algo(knn).params({
        node_id: 1,
        node_schema_property: ['d1', 'd2', 'd3', 'd4'],
        top_k: 4,
        target_schema_property: @image.type
      }) as a1, a2 
      return a1, a2
      

      Results: a1 and a2

      attribute_value count
      Gold 2
      node similarity
      4 0.538974677919475
      3 0.705071517140301
      6 0.841922130134788
      2 0.855159652306166

      Stream Return

      Alias Ordinal
      Type
      Description
      Columns
      0 KV The elected class label and its number of occurrences among the k nearest neighbors attribute_value, count
      algo(knn).params({
        node_id: 2,
        node_schema_property: ['@image.d1', '@image.d2', '@image.d3', '@image.d4'],
        top_k: 5,
        target_schema_property: @image.type
      }).stream() as label
      find().nodes({_uuid == 2}) as target
      return case
        when target.type == label.attribute_value then 'True'
        else 'false'
      end
      

      Results: false

      find().nodes({@image}) as images
      call {
          with images._uuid as target
          algo(knn).params({
            node_id: target,
            node_schema_property: ['d1', 'd2', 'd3', 'd4'],
            top_k: 3,
            target_schema_property: 'type'
          }).stream() as label
          return label
      }
      return table(images._id, label.attribute_value)
      

      Results: table(images._id, label.attribute_value)

      images._id label.attribute_value
      image1 Silver
      image2 Silver
      image3 Gold
      image4 Silver
      image5 Gold
      image6 Gold
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