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Distance metrics

Available distance metrics

If not specified explicitly, the default distance metric in Weaviate is cosine. It can be set in the vectorIndexConfig field as part of the schema (example) to any of the following types:

Comparing distances

In all cases, larger distance values indicate lower similarity. Conversely, smaller distance values indicate higher similarity.

cosineCosine (angular) distance.
[See note 1 below]
1 - cosine_sim(a,b)0 <= d <= 20: identical vectors

2: Opposing vectors.
dotA dot product-based indication of distance.

More precisely, the negative dot product.
[See note 2 below]
-dot(a,b)-∞ < d < ∞-3: more similar than -2

2: more similar than 5
l2-squaredThe squared euclidean distance between two vectors.sum((a_i - b_i)^2)0 <= d < ∞0: identical vectors
hammingNumber of differences between vectors at each dimensions.sum(|a_i != b_i|)0 <= d < ∞0: identical vectors
manhattanThe distance between two vector dimensions measured along axes at right angles.sum(|a_i - b_i|)0 <= d < dims0: identical vectors

If you're missing your favorite distance type and would like to contribute it to Weaviate, we'd be happy to review your PR.

Additional notes
  1. If cosine is chosen, all vectors are normalized to length 1 at read time and dot product is used to calculate the distance for computational efficiency.
  2. Dot Product on its own is a similarity metric, not a distance metric. As a result, Weaviate returns the negative dot product to stick with the intuition that a smaller value of a distance indicates a more similar result and a higher distance value indicates a less similar result.

Distance implementations and optimizations

On a typical Weaviate use case the largest portion of CPU time is spent calculating vector distances. Even with an approximate nearest neighbor index - which leads to far fewer calculations - the efficiency of distance calculations has a major impact on overall performance.

You can use the following overview to find the best possible combination of distance metric and CPU architecture / instruction set.

Distancelinux/amd64 AVX2darwin/amd64 AVX2linux/amd64 AVX512linux/arm64darwin/arm64
cosineoptimizedoptimizedno SIMDno SIMDno SIMD
dotoptimizedoptimizedno SIMDoptimized
From v1.21
From v1.21
l2-squaredoptimizedoptimizedno SIMDoptimized
From v1.21
From v1.21
hammingno SIMDno SIMDno SIMDno SIMDno SIMD
manhattanno SIMDno SIMDno SIMDno SIMDno SIMD

If you like dealing with Assembly programming, SIMD, and vector instruction sets we would love to receive your contribution for one of the combinations that have not yet received an SIMD-specific optimization.

Distance fields in the APIs

The distance is exposed in the APIs in two ways:

  • Whenever a vector search is involved, the distance can be displayed as part of the results, for example using _additional { distance }
  • Whenever a vector search is involved, the distance can be specified as a limiting criterion, for example using nearVector({distance: 1.5, vector: ... })

Note: The distance field was introduced in v1.14.0. In previous versions, only certainty (see below) was available.

Distance vs Certainty

Prior to version v1.14 only certainty was available in the APIs. The original ideas behind certainty was to normalize the distance score into a value between 0 <= certainty <= 1, where 1 would represent identical vectors and 0 would represent opposite vectors.

This concept is however unique to cosine distance. With other distance metrics, scores may be unbounded. As a result the preferred way is to use distance in favor of certainty.

For backward compatibility, certainty can still be used when the distance is cosine. If any other distance is selected certainty cannot be used.

See also distance and certainty _additional{} properties.

Questions and feedback

If you have any questions or feedback, let us know in the user forum.