Sparse Vector: `svector`

Unlike dense vectors, sparse vectors are very high-dimensional but contain few non-zero values.

Typically, sparse vectors can be created from:

• Word co-occurrence matrices
• Term frequency-inverse document frequency (TF-IDF) vectors
• User-item interaction matrices
• Network adjacency matrices

Sparse vectors in pgvecto.rs are called svector.

Here’s an example of creating a table with a svector column and inserting values:

CREATE TABLE items (
  id bigserial PRIMARY KEY,
  embedding svector(10) NOT NULL
);

INSERT INTO items (embedding) VALUES ('[0.1,0,0,0,0,0,0,0,0,0]'), ('[0,0,0,0,0,0,0,0,0,0.5]');

Index can be created on svector type as well.

CREATE INDEX your_index_name ON items USING vectors (embedding svector_l2_ops);

SELECT * FROM items ORDER BY embedding <-> '[0.3,0,0,0,0,0,0,0,0,0]' LIMIT 1;

We support three operators to calculate the distance between two svector values.

• <-> (svector_l2_ops): squared Euclidean distance, defined as $\Sigma (x_i - y_i) ^ 2$.
• <#> (svector_dot_ops): negative dot product, defined as $- \Sigma x_iy_i$.
• <=> (svector_cos_ops): cosine distance, defined as $1 - \frac{\Sigma x_iy_i}{\sqrt{\Sigma x_i^2 \Sigma y_i^2}}$.

There is also a function to_svector to create a svector. It will set the value at the specified position.

-- to_svector(dim: INTEGER, position: ARRAY, value: ARRAY) -> svector
SELECT to_svector(5, '{0, 4}', '{0.3, 0.5}');
-- [0.3, 0, 0, 0, 0.5]