พื้นฐานตัวชี้วัดระยะห่างและการสร้างดัชนี

A vector DB finds vectors close to your query, but 'close' is defined by a distance metric — and the metric you pick shapes what counts as similar.

Euclidean (L2) distance is the straight-line distance between two points: smaller means closer. Run the example to see it.

Cosine similarity measures the angle between vectors, ignoring magnitude. It's the go-to for text embeddings, since direction carries the meaning.

The dot product blends angle and magnitude. With normalized vectors it equals cosine similarity — which is why many systems normalize, then use dot product for speed.

Match the metric to what your model was trained for: text usually cosine, normalized vectors dot product, some image or geo data Euclidean. A mismatch silently hurts results.

Brute force — comparing the query to every stored vector — is exact but slow: millions of vectors mean millions of comparisons per query. It doesn't scale.

ANN indexes trade a sliver of accuracy for massive speed by cleverly skipping most candidates. Recall stays high while latency drops by orders of magnitude.

HNSW builds a layered graph you navigate coarse to fine for excellent recall and speed — the default in many vector DBs, tunable via ef and M.

IVF clusters vectors into buckets and only searches the ones nearest your query. Fewer probes mean faster search, at a small accuracy cost.

Every ANN index exposes knobs that trade recall for speed. Searching more candidates raises both recall and latency. Tune to your accuracy target, then push speed.

Putting it together: pick the right distance metric for your embeddings, then use an ANN index (HNSW or IVF) to query fast at scale, tuning the recall-speed knobs.

Test your understanding of metrics and indexes.

Recap: the core distance metrics (Euclidean, cosine, dot product) — text usually cosine — plus ANN indexes like HNSW and IVF that trade a little recall for big speed.