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> From there you can used pgvector's cosine distance operator for searching for related documents How does this scale with the number of rows in the database?

> From there you can used pgvector's cosine distance operator for searching for related documents How does this scale with the number of rows in the database? My first thoughts are that this is O(n). Does the pgvector have a smarter implementation that allows performing k-nearest neighbor searches efficiently?

pedrosorio 4y ago
You can add indexes per distance function to perform fast approximate nearest neighbor search: https://github.com/pgvector/pgvector#indexing https://github.com/pgvector/pgvector#indexing They mention this paper in the references: https://dl.acm.org/doi/pdf/10.1145/3318464.3386131 https://dl.acm.org/doi/pdf/10.1145/3318464.3386131
anon291 4y ago
locality sensitive hashing is the typical method here. You generate a ton of random vectors. These vectors automatically give rise to infinite hyperplanes (the one they are normal to). Each vector/hyperplane is associated with a bit in the final hash. Then, each input vector is hashed by setting the bit if it's on one side of the hyperplane or unsetting it if it's on the other. The hamming distance between two vectors is now correlated with the cosine similarity. Or something like that.
- kekub 4y ago
  That's the reason I come to HN every day. Thanks for the explanation, which probably could not be more compact.
- justjonathan 4y ago
  That’s so smart! I read stuff like that and I’m just in awe of the cleverness.
ec109685 4y ago
They describe optimizations here as well: https://simonwillison.net/2023/Jan/13/semantic-search-answers/ https://simonwillison.net/2023/Jan/13/semantic-search-answer...