$similarityEuclidean (expression operator)

Definition

$similarityEuclidean

Returns the Euclidean distance between two numeric vectors represented as arrays or binData values. Euclidean distance measures the straight-line distance between two points in vector space.

$similarityEuclidean has two syntax forms.

Concise syntax returns a raw Euclidean distance:

{ $similarityEuclidean: [ <vector1>, <vector2> ] }

Full syntax accepts an optional normalization parameter:

{
   $similarityEuclidean: {
      vectors: [ <vector1>, <vector2> ],
      score: <boolean>
   }
}

When using the full syntax, $similarityEuclidean accepts the following fields:

Field	Type	Necessity	Description
vectors	Array	Required	Array of exactly two expressions. Each expression must resolve to an array of numeric values or a binData value. Both vectors must have equal length.
score	Boolean	Optional	When true, returns a normalized score in the range (0, 1] using the formula 1 / (1 + distance). Identical vectors produce a score of 1. Defaults to false.

For more information on expressions, see Expressions.

Behavior

Example

The following example uses a vectors collection:

db.vectors.insertMany( [
   { _id: 1, a: [1, 2, 3], b: [1, 2, 3] },
   { _id: 2, a: [1, 2, 3], b: [3, 2, 1] },
   { _id: 3, a: [1, 2, 3], b: [4, 5, 6] }
] )

The following aggregation pipeline computes the Euclidean distance between the a and b fields for each document and returns both the raw distance and the normalized score:

db.vectors.aggregate( [
   {
      $project: {
         raw: { $similarityEuclidean: [ "$a", "$b" ] },
         normalized: {
            $similarityEuclidean: {
               vectors: [ "$a", "$b" ],
               score: true
            }
         }
      }
   }
] )

The operation returns the following results:

{ _id: 1, raw: 0, normalized: 1 }
{ _id: 2, raw: 2.8284271247461903,
  normalized: 0.2612038749637415 }
{ _id: 3, raw: 5.196152422706632,
  normalized: 0.16139702886038895 }

Learn More

• $vectorSearch

• Expressions