EUCLIDEAN_DISTANCE
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The EUCLIDEAN_
function returns the euclidean distance between two vector values.EUCLIDEAN_
takes as input two vectors and returns a numeric value.
A common use of EUCLIDEAN_
is to calculate the similarity between vectors (vector similarity), which is used in semantic text search, generative AI, searches of images and audio files, and other applications.EUCLIDEAN_
is to find a set of vectors that most closely match a query vector.
See Working with Vector Data for more information about using vectors in SingleStore.
Syntax
EUCLIDEAN_DISTANCE(vector_expression, vector_expression)
Arguments

vector_
: An expression that evaluates to a vector.expression Vectors can be stored in SingleStore using the BLOB
type (BLOB Types).
Remarks

If the result is infinity, negative infinity, or not a number (NaN),
NULL
will be returned instead. 
The default element type for vector storage and processing is 32bit floatingpoint (
F32
).The EUCLIDEAN_
function assumes the vector inputs are encoded as 32bit floatingpoint numbers and returns aDISTANCE DOUBLE
. 
EUCLIDEAN_
is computationally equivalent toDISTANCE(v1, v2) SQRT(DOT_
.PRODUCT(VECTOR_ SUB(v1, v2), VECTOR_ SUB(v1, v2))) However, the EUCLIDEAN_
function is more efficient than the latter.DISTANCE() 
To execute this function, the host processor must support AVX2 instruction set extensions.
If AVX2 is not supported, an error will occur during execution.
Using EUCLIDEAN_DISTANCE with Vectors as BLOBs
The following example shows the use of EUCLIDEAN_
to calculate the similarity between a query vector and a set of vectors in a table with the vectors stored as BLOBs.
Create a table with a column of type BLOB
to store the vectors.vec
and type BLOB
, will store the vectors.BLOB
s, hence the column of type BLOB
named vec
.
Then insert data using the JSON_
builtin function to easily insert properly formatted vectors.
CREATE TABLE vectors_b (id int, vec BLOB not null);INSERT INTO vectors_b VALUES (1, JSON_ARRAY_PACK('[0.1, 0.8, 0.2, 0.555]'));INSERT INTO vectors_b VALUES (2, JSON_ARRAY_PACK('[0.45, 0.55, 0.495, 0.5]'));
Use the HEX()
builtin function to return a printable form of the binary data:
SELECT HEX(vec) FROM vectors_b;
++
 HEX(vec) 
++
 6666E63ECDCC0C3FA470FD3E0000003F 
 CDCCCC3DCDCC4C3FCDCC4C3E7B140E3F 
++
Query the table using the EUCLIDEAN_
function in a SELECT
statement.
The SQL below sets up query vector (@query_
) and then calculates the EUCLIDEAN_
of the query vector and the vectors in the vectors_
table.
SET @query_vec = JSON_ARRAY_PACK('[0.44, 0.554, 0.34, 0.62]');SELECT EUCLIDEAN_DISTANCE(vec, @query_vec) AS scoreFROM vectors_b;
++
 score 
++
 0.19631861943383927 
 0.44714763700937277 
++
EUCLIDEAN_DISTANCE() with JSON_ARRAY_PACK()
The JSON_
function makes it easier to input properlyformatted vectors.JSON_
should be used when loading vectors into tables as is shown in the example below.JSON_
at the time they are loaded into a table so that the data stored in the BLOB
attribute in the table is in packed binary format.
JSON_
should not normally be used as an argument to the EUCLIDEAN_
function except when JSON_
is being used to build a constant vector value as is shown in the query below.
SELECT EUCLIDEAN_DISTANCE(JSON_ARRAY_PACK('[0.44, 0.554, 0.34, 0.62]'), vec) AS scoreFROM vectors_bORDER BY score ASC;
++
 score 
++
 0.19631861943383927 
 0.44714763700937277 
++
Using EUCLIDEAN_DISTANCE in Filters, Joins, and Ordering
EUCLIDEAN_
can appear wherever a floatingpoint expression can be used in a query, including in filters, ordering, joins, and cross products.
Use the vectors_
table and the @query_
created above, in addition to the new table created below, when running the following query.
The following query uses EUCLIDEAN_
in the SELECT
clause, names it "score," and then filters on the score in the WHERE
clause.EUCLIDEAN_
, of that vector with respect to @query_
.
SET @query_vec = JSON_ARRAY_PACK('[0.44, 0.554, 0.34, 0.62]');SELECT EUCLIDEAN_DISTANCE(vec, @query_vec) AS scoreFROM vectors_bWHERE score < 0.7ORDER BY score ASC;
++
 score 
++
 0.19631861943383927 
 0.44714763700937277 
++
CREATE TABLE vectors_2b (id_2 int, vec_2 BLOB not null);INSERT INTO vectors_2b VALUES (5, JSON_ARRAY_PACK('[0.4, 0.49, 0.16, 0.555]'));INSERT INTO vectors_2b VALUES (6, JSON_ARRAY_PACK('[0.01, 0.1, 0.2, 0.975]'));
Formatting Binary Vector Data for BLOBs
When using the BLOB
type for vector operations, vector data can be formatted using JSON_
.BLOB
s.BLOB
containing packed numbers in littleendian byte order.BLOB
s can be of any length; however, the input blob length must be divisible by the size of the packed vector elements (1, 2, 4 , or 8 bytes, depending on the vector element).
Related Topics
Last modified: June 3, 2024