COSINE_SIMILARITY

Returns the cosine similarity of two n-dimensional vectors. Cosine similarity is the cosine of the angle between two non-zero vectors. A returned value of 1 means that the vectors are identical, a value of 0 means the vectors are orthogonal, and a value of -1 means that the vectors are opposites.

Behavior type

Syntax

COSINE_SIMILARITY( vector_arr1, vector_arr2 )

Arguments

vector_arr1

N-dimensional vector, type ARRAY of INT, FLOAT, NUMERIC

vector_arr2

N-dimensional vector, type ARRAY of INT, FLOAT, NUMERIC

For input vector arrays that have a norm of 0, the following logic is used:

• If both vectors are 0, then a value of 1 is returned as they are identical.
• If only one of the vectors is 0, then a value of 0 is returned as the vectors are orthogonal (zero similarity).

Returns

FLOAT

Examples

The following example computes the cosine similarity for two vector arrays:

SELECT id, vector_arr1, vector_arr2, COSINE_SIMILARITY(vector_arr1, vector_arr2) AS similarity FROM vectors_array;
id |  vector_arr1  |  vector_arr2  |    similarity     
----+---------------+---------------+-------------------
  1 | [1.0,2.0,3.0] | [4.0,5.0,6.0] | 0.974631846197076
  2 | [1.5,2.5,3.5] | [4.5,5.5,6.5] | 0.985871023540107
  3 | [0.0,1.0,0.0] | [0.0,0.0,1.0] |                 0
  4 | [2.0,0.0,0.0] | [0.0,2.0,0.0] |                 0
  5 | [1.0,1.0,1.0] | [1.0,1.0,1.0] |                 1
(5 rows)

The following example computes the cosine similarity for a 5D vector:

SELECT COSINE_SIMILARITY(Array[1.0, 2.0, 3.0, 4.0, 5.0], Array[1.0, 2.0, 3.0, 3.0, 4.0]);
COSINE_SIMILARITY
-------------------
  0.99321708930132
(1 row)