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.
SingleStore supports a native vector data type and indexed approximatenearestneighbor (ANN) search that provide highperformance vector search and easier building of vectorbased applications.
See Vector Type, Vector Indexing, and Working with Vector Data for more information about using vectors in SingleStore.
Syntax
vector_expression <> vector_expressionEUCLIDEAN_DISTANCE(vector_expression, vector_expression)
Arguments

vector_
: An expression that evaluates to a vector.expression Vectors can be stored in SingleStore using the native VECTOR
data type (Vector Type) or theBLOB
data type (BLOB Types).SingleStorerecommends using the VECTOR
data type when possible.
Remarks

If the result of
EUCLIDEAN_
is infinity, negative infinity, or not a number (NaN), NULL will be returned instead.DISTANCE() 
The default format for vector element storage and processing is 32bit floating point number (
FLOAT
).The EUCLIDEAN_
function assumes the vector inputs are encoded as 32bit floating point numbers and returns aDISTANCE DOUBLE
. 
See Using Other Numeric Element Types for information on using
EUCLIDEAN_
with vectors with element types other than 32bit floating point numbers.DISTANCE 
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 the VECTOR Data Type
The following example shows the use of EUCLIDEAN_
to calculate the similarity between a query vector and a set of vectors in a table.
Create a table with a column of type VECTOR
, insert data into the table, and then verify the contents of the table.
CREATE TABLE vectors (id int, vec VECTOR(4) not null);INSERT INTO vectors VALUES (1, '[0.45, 0.55, 0.495, 0.5]');INSERT INTO vectors VALUES (2, '[0.1, 0.8, 0.2, 0.555]');INSERT INTO vectors VALUES (3, '[0.5, 0.03, 0.1, 0.86]');INSERT INTO vectors VALUES (4, '[0.5, 0.3, 0.807, 0.1]');
SELECT id, vecFROM vectorsORDER BY id;
+++
 id  vec 
+++
 1  [0.449999988,0.550000012,0.495000005,0.5] 
 2  [0.100000001,0.800000012,0.200000003,0.555000007] 
 3  [0.5,0.0299999993,0.100000001,0.860000014] 
 4  [0.5,0.300000012,0.806999981,0.100000001] 
+++
Notice that the results of the SELECT
do not exactly match the values in the INSERT
.VECTOR
data type are stored as floating point numbers and the values in the INSERT
statement are not perfectly representable in floating point.
After you've created a table and inserted data, set up a query vector.vectors
table and @query_
.
SET @query_vec = '[0.44, 0.554, 0.34, 0.62]' :> VECTOR(4);
This query finds the similarities between vectors and @query_
using using the EUCLIDEAN_
infix operator <>
.ORDER BY
clause is included so the order of your results match the results shown below.
SELECT vec <> @query_vec AS scoreFROM vectorsORDER BY score ASC;
++
 score 
++
 0.19631861943383927 
 0.44714763700937277 
 0.7460596366393402 
 1.2148481657187131 
++
Using EUCLIDEAN_DISTANCE (<>) in Filters, Joins, and Ordering
EUCLIDEAN_
can appear wherever a floating point expression can be used in a query, including in filters, ordering, joins and cross products.
The DOT_DOT_
in various ways in SQL queries.EUCLIDEAN_
can be used similarly.ASC
when using EUCLIDEAN_
and DESC
with DOT_
.
Below is one example of using EUCLIDEAN_
(<>
) in a join query.
Use the vectors
table and the @query_
created above, in addition to the new table created below, when running the following query.
CREATE TABLE vectors_2 (id_2 int, vec_2 VECTOR(4) not null);INSERT INTO vectors_2 VALUES (5, '[0.4, 0.49, 0.16, 0.555]');INSERT INTO vectors_2 VALUES (6, '[0.01, 0.1, 0.2, 0.975]');
SELECT v1.id, v2.id_2, v1.vec <> v2.vec_2 AS scoreFROM vectors v1, vectors_2 v2 WHERE v1.vec <> v2.vec_2 < 0.7ORDER BY score ASC;
++++
 id  id_2  score 
++++
 1  5  0.34835327652980475 
 2  5  0.4332435843558954 
 3  6  0.5179044162849211 
++++
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
.
CREATE TABLE vectors_b (id int, vec BLOB not null);
Use the JSON_
builtin function to easily insert properly formatted vectors.
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.
First, set up a query vector.
SET @query_vec = JSON_ARRAY_PACK('[0.44, 0.554, 0.34, 0.62]');
Now, write a query that calculates the EUCLIDEAN_
of the query vector and vectors in the vectors_
table.
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 DOT_
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_b;
++
 score 
++
 0.19631861943383927 
 0.44714763700937277 
++
Note
It is not recommended to use the EUCLIDEAN_
infix operator (<>
) with vectors stored as BLOB
s.BLOB
data, the infix operator (<>
) will interpret vector elements as 32bit floating point numbers.
Using Other Numeric Element Types
The default format for vector element storage and processing is 32bit floating point number (FLOAT
).EUCLIDEAN_
and JSON_
functions to specify other types for the vector elements._
.
Below is an example of using JSON_
and EUCLIDEAN_
with 16bit signed integers.
CREATE TABLE vectors_i (id int, vec BLOB not null);INSERT INTO vectors_i VALUES (1, JSON_ARRAY_PACK_I16('[1, 3, 2, 5]'));INSERT INTO vectors_i VALUES(2, JSON_ARRAY_PACK_I16('[23, 4, 1, 8]'));SET @query_vec = JSON_ARRAY_PACK_I16('[4, 5, 4, 2]');
SELECTEUCLIDEAN_DISTANCE_I16(@query_vec, vec) as EuclidDistFROM vectors_i;
++
 EuclidDist 
++
 5.0990195135927845 
 20.174241001832016 
++
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
It is important that you use the EUCLIDEAN_
function that matches the encoding of the input vectors and that the encodings of the input vectors match.EUCLIDEAN_
should be used with vectors that have been encoded with JSON_
, and both input vectors must be encoded as I16
.
The table below lists the suffixes and associated data types.
Suffix 
Datatype 


8bit signed integer 

16bit signed integer 

32bit signed integer 

64bit signed integer 

32bit floatingpoint number (IEEE standard format) 

64bit floatingpoint number (IEEE standard format) 
Formatting Binary Vector Data for BLOBs
When using the BLOB
data type for EUCLIDEAN_
operations, the 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: March 1, 2024