Categories:: Vector similarity functions

VECTOR_L1_DISTANCE¶

Computes the L1 distance between two vectors.

L1 distance, also known as the Taxicab or Manhattan distance, is a measure of the distance between two points in a vector space. The distance is calculated by taking the sum of the absolute value of the differences of vector elements. The result is a value of zero or higher. If the distance is zero, the vectors are identical. The larger the distance, the farther apart the vectors are.

See also:: VECTOR_INNER_PRODUCT , VECTOR_L2_DISTANCE , VECTOR_COSINE_SIMILARITY , Vector Embeddings

Syntax¶

VECTOR_L1_DISTANCE( <vector>, <vector> )

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Arguments¶

vector: The VECTOR value to calculate the distance from.
vector: The VECTOR value to calculate the distance to.

Returns¶

Returns the L1 distance between the two input vectors as a FLOAT value.

Usage notes¶

Due to computational optimizations in the vector comparison functions, floating-point errors may be slightly larger than usual (e.g. about 1e-4).

Examples¶

This example uses the VECTOR_L1_DISTANCE function to determine which vectors in the table are closest to each other between columns a and b:

CREATE TABLE vectors (a VECTOR(FLOAT, 3), b VECTOR(FLOAT, 3));
INSERT INTO vectors SELECT [1.1,2.2,3]::VECTOR(FLOAT,3), [1,1,1]::VECTOR(FLOAT,3);
INSERT INTO vectors SELECT [1,2.2,3]::VECTOR(FLOAT,3), [4,6,8]::VECTOR(FLOAT,3);

SELECT VECTOR_L1_DISTANCE(a, b) FROM vectors;

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+--------------+
| 3.300000191  |
|--------------|
| 11.800000191 |
+--------------+