Pearson Correlation Coefficient

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 to the product of their standard deviations:

The Pearson correlation coefficient ranges from -1 to 1:

Considerations

• Theoretically, the calculation of Pearson correlation coefficient between two nodes is independent of their connectivity.

Example Graph

GQL
INSERT (:product {_id:"product1", price:50, weight:160, width:20, height:152}),
       (:product {_id:"product2", price:42, weight:90, width:30, height:90}),
       (:product {_id:"product3", price:24, weight:50, width:55, height:70}),
       (:product {_id:"product4", price:38, weight:20, width:32, height:66})

Parameters

Supports three computation modes:

• All-pairs: When both ids and ids2 are empty, computes similarity between all node pairs in the graph.
• Pairing: When both ids and ids2 are specified, computes similarity between each node in ids and each node in ids2.
• Selection: When only ids is specified (no ids2), computes similarity between each node in ids and all other nodes. Use top_limit to limit results per source node.

Run Mode

GQL
CALL algo.similarity({
  type: "pearson",
  ids: ["product1", "product2"],
  ids2: ["product2", "product3", "product4"],
  node_property: ["price", "weight", "width", "height"],
  order: "desc"
}) YIELD node1, node2, similarity

Result:

Stream Mode

GQL
CALL algo.similarity.stream({
  type: "pearson",
  ids: ["product1", "product3"],
  node_property: ["price", "weight", "width", "height"],
  top_limit: 1,
  order: "desc"
}) YIELD node1, node2, similarity
RETURN node1, node2, similarity

Stats Mode

Returns:

GQL
CALL algo.similarity.stats({
  type: "pearson",
  node_property: ["price", "weight", "width", "height"]
}) YIELD pairCount, minSimilarity, maxSimilarity, avgSimilarity

Result:

Write Mode

Computes results and writes them back to node properties.

Write parameters:

Returns:

GQL
CALL algo.similarity.write({
  type: "pearson",
  ids: ["product1"],
  node_property: ["price", "weight", "width", "height"]
}, {
  db: {
    property: "sim_score"
  }
}) YIELD task_id, nodesWritten, computeTimeMs, writeTimeMs