COSINE_SIMILARITY
Description
Calculates the cosine similarity between two vectors.
The similarity is computed from the dot product and vector norms, and the result is in [-1, 1].
Syntax
COSINE_SIMILARITY(<array1>, <array2>)
Parameters
| Parameter | Description |
|---|---|
<array1> | The first vector. The input type must be ARRAY<FLOAT>. |
<array2> | The second vector. The input type must be ARRAY<FLOAT>, and the number of elements must be the same as <array1>. |
Return Value
Returns the cosine similarity between two vectors, in FLOAT type.
If the input array is NULL, or any element in the array is NULL, an error is returned.
If the two arrays have different numbers of elements, an error is returned.
If the array is empty, or either vector is a zero vector, 0.0 is returned.
Example
-- Two identical vectors have similarity 1
SELECT COSINE_SIMILARITY([1, 2, 3], [1, 2, 3]);
+-----------------------------------------+
| COSINE_SIMILARITY([1, 2, 3], [1, 2, 3]) |
+-----------------------------------------+
| 1 |
+-----------------------------------------+
[1, 2, 3] and [1, 2, 3] point in the same direction, so the similarity is 1.
-- Orthogonal vectors have similarity 0
SELECT COSINE_SIMILARITY([1, 0], [0, 1]);
+-----------------------------------+
| COSINE_SIMILARITY([1, 0], [0, 1]) |
+-----------------------------------+
| 0 |
+-----------------------------------+
The vectors are orthogonal, so their dot product is 0 and the similarity is 0.
-- A zero vector returns 0
SELECT COSINE_SIMILARITY([0, 0, 0], [1, 2, 3]);
+-----------------------------------------+
| COSINE_SIMILARITY([0, 0, 0], [1, 2, 3]) |
+-----------------------------------------+
| 0 |
+-----------------------------------------+
A zero vector has no valid direction, so the result is 0.
-- An empty array returns 0
SELECT COSINE_SIMILARITY([], []);
+---------------------------+
| COSINE_SIMILARITY([], []) |
+---------------------------+
| 0 |
+---------------------------+
-- NULL inside the input array raises an error
SELECT COSINE_SIMILARITY([1, NULL, 3], [1, 2, 3]);
ERROR 1105 (HY000): errCode = 2, detailMessage = (127.0.0.1)[INVALID_ARGUMENT]First argument for function cosine_similarity cannot have null
