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. 
See Using Suffixes for Other Element Types with BLOBs for information on using
EUCLIDEAN_
with vectors with element types other than 32bit floatingpoint numbers.DISTANCE 
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()
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]'));
To demonstrate the contents of the table, use the JSON_
function to return the table elements in JSON format:
SELECT JSON_ARRAY_UNPACK(vec) FROM vectors_b;
++
 JSON_ARRAY_UNPACK(vec) 
++
 [0.449999988,0.550000012,0.495000005,0.5] 
 [0.100000001,0.800000012,0.200000003,0.555000007] 
++
You can also 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 
++
EUCLIDEAN_
can even be used in cross products and joins – both arguments to it can be table fields or derived from table fields.
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]'));
SELECT v1.id, v2.id_2, EUCLIDEAN_DISTANCE(v1.vec, v2.vec_2) AS scoreFROM vectors_b v1, vectors_2b v2WHERE EUCLIDEAN_DISTANCE (v1.vec, v2.vec_2)<0.7ORDER BY score ASC;
++++
 id  id_2  score 
++++
 2  5  0.34835327652980475 
 1  5  0.4332435843558954 
++++
Using Suffixes for Other Element Types with BLOBs
The default element type for vector storage and processing is 32bit floating point (F32
).
You can specify the datatype of the vector elements to be used in the operation by adding a suffix to the function._
.
When using a suffix, the return type will be the type of the suffix.
The following table lists the suffixes and their data type.
Suffix 
Data Type 


8bit signed integer 

16bit signed integer 

32bit signed integer 

64bit signed integer 

32bit floatingpoint number (IEEE standard format) 

64bit floatingpoint number (IEEE standard format) 
EUCLIDEAN_DISTANCE on BLOBs with 16bit Integers
Below is an example of using JSON_
and EUCLIDEAN_
with 16bit signed integers.
CREATE TABLE vectors_b_i (id int, vec BLOB not null);INSERT INTO vectors_b_i VALUES (1, JSON_ARRAY_PACK_I16('[1, 3, 2, 5]'));INSERT INTO vectors_b_i VALUES(2, JSON_ARRAY_PACK_I16('[23, 4, 1, 8]'));
SET @qv = JSON_ARRAY_PACK_I16('[1, 2, 3, 4]');SELECT EUCLIDEAN_DISTANCE_I16(@qv, vec) as EuclidDistFROM vectors_b_i;
++
 EuclidDist 
++
 22.538855339169288 
 1.7320508075688772 
++
The result is an integer as indicated by the _
suffix.
When using suffixed versions of EUCLIDEAN_
, the return type will be the type of the suffix.
Note
Be sure that the suffixes you use to pack the vector data match the suffixes you use to unpack the data and the suffixes you use on functions to process that data.
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: August 14, 2024