duckdb-vector

A duckdb extension to add support for vectors(not the duckdb internal representation).

Vector Distance

This extension adds support for vector distances using the function list_distance. The third argument to this function is the distance algorithm to be used. Note: The distance algorithm should be a binary aggregate. Eg:

SELECT list_distance([1, 1, 1], [1, 1, 3], 'dot_product') FROM vectors;
----
5

You can also use the macro for this which is of the form list_<distance_algorithm>.

The following distance algorithms are supported:

1. l2distance or euclidean_distance: $\sqrt{\sum_{i=1}^n {(y_i - x_i)}^2}$
2. dot_product: $\sum_{i=1}^{n}x_iy_i$
3. cosine_similarity: $\frac{\sum_{i=1}^{n}x_ib_i}{\sqrt{{\sum_{i=1}^{n}{x_i}^2}{\sum_{i=1}^{n}{y_i}^2}}}$
4. cosine_distance: $1 - cosineSimilarity$ or $1 - \frac{\sum_{i=1}^{n}x_ib_i}{\sqrt{{\sum_{i=1}^{n}{x_i}^2}{\sum_{i=1}^{n}{y_i}^2}}}$
5. l2norm: $\sqrt{\sum_{i=1}^n {x_i}^2}$ (Since this is a unary aggregate function, it can be used with list_aggr or list_l2norm).