Overview

k-Nearest Neighbors (kNN) algorithm, also known as the nearest neighbors algorithm, classifies a given sample based on the classifications of its K most similar (e.g. Cosine Similarity) samples. Proposed in 1967 by IEEE members T. M. Cover and P. E. HART, this algorithm is one of the simplest data classification techniques.

Although contains the word 'neighbor' in its name, kNN does not rely on the relationship between samples when calculating similar samples, in graph it means that kNN has nothing to do with the edges between nodes.

Related material of the algorithm:

• T.M. Cover, P.E. Hart, Nearest Neighbor Pattern Classification (1967)

Basic Concept

Select Similar Nodes

Ultipa's kNN algorithm defines the sample as node in the graph and uses cosine similarity (read the chapter Cosine Similarity) between nodes as the similarity between the samples, then to select K nodes y that are most similar to the given node x as the K nearest neighbors Kx.

Vote on Classification

Using one node property as the classification label, and count the labels of the selected K nearest neighbors, and the label with the most occurrences will be used as the label of x:

If there are more than one labels that appear the most, the label of the node which has the highest similarity will be used.

Special Case

Lonely Node, Disconnected Graph

Theoretically, the calculation of kNN does not depend on the existence of edges in the graph, and regardless of whether the node to be calculated is lonely node or which connected component it locates, it does not affect the calculation of kNN.

Self-loop Edge

The calculation of kNN has nothing to do with edges.

Directed Edge

The calculation of kNN has nothing to do with edges.

Results and Statistics

The graph below has 5 product nodes (edges are ignored), product node has properties price, weight, weight and height:

Algorithm results: Given node product1, select the most similar 3 nodes based on properties price, weight and width, and specify property height as the classification label

• The voted classification label attribute_value and the number of times count it appears in the 3 kNN

• The selected 3 kNN node and its cosine similarity similarity between product1

Note: The cosine similarity between product5 and product1 is 0.404234826778782, thus it is not involved in the 3 kNN.

Algorithm statistics: N/A

Command and Configuration

• Command: algo(knn)
• Configurations for the parameter params():

Example: Estimate the value of height according to the property price, weight and width of node UUID = 1

algo(knn).params({
  node_id: 1,
  node_schema_property: [@product.price,@product.weight,@product.width],
  top_k: 4,
  target_schema_property: @product.height
}) as height return height

Algorithm Execution

Task Writeback

1. File Writeback

Example: Estimate the value of height according to property price, weight and width of node UUID = 1, write the algorithm results back to file named knn

algo(knn).params({
  node_id: 1,
  node_schema_property: [@product.price,@product.weight,@product.width],
  top_k: 4,
  target_schema_property: @product.height
}).write({
  file:{
    filename: "knn"
    }
})

2. Property Writeback

Not supported by this algorithm.

3. Statistics Writeback

Not supported by this algorithm.

Direct Return

Example: Estimate the value of height according to property price, weight and width of node UUID = 1, define algorithm results as alias named a1 and a2 and return the results

algo(knn).params({
  node_id: 1,
  node_schema_property: [@product.price,@product.weight,@product.width],
  top_k: 3,
  target_schema_property: @product.height
}) as a1, a2 return a1, a2

Streaming Return

Example: Estimate the value of height according to property price, weight and width of node UUID = 1 and update the value of height of the node

algo(knn).params({
  node_id: 1,
  node_schema_property: [@product.price,@product.weight,@product.width],
  top_k: 3,
  target_schema_property: @product.height
}).stream() as a1
with a1.attribute_value as value
update().nodes(1).set({height: value})

Real-time Statistics

This algorithm has no statistics.