Choosing Between Cosine Similarity, Dot Product, and Euclidean Distance for RAG Applications

Understanding Vector Similarity

If you're interested in real-world uses cases for distance measures check out our great post on the subject here: Real Use Cases for Cosine Similarity, Dot Product, and Euclidean Distance

In RAG workflows, we store document or text embeddings as vectors in a database. When we want to retrieve the most relevant items from our stored vectors, we need a way to measure how close (or similar) these vectors are to each other. Three common approaches are:

Cosine Similarity
Dot Product
Euclidean Distance

Below, we’ll walk through each method, when to use it, and give a quick illustration to solidify the concept.

1. Cosine Similarity

Cosine similarity looks at the angle between two vectors rather than their overall magnitude. Imagine you have two arrows on a dartboard. The difference in their directions (angles) tells you how “similar” they are, irrespective of how long each arrow is.

When to Use Cosine Similarity

Comparing Text Documents: Often used in NLP tasks because two documents can be similar in topic (direction of the arrow) even if one is much longer than the other (length of the arrow).
Ignoring Magnitude Differences: If you only care about the direction or overall pattern, cosine similarity is a strong choice.

Cosine Similarity Example

Suppose you have a short marketing blurb and a lengthy press release on the same subject. Their word counts differ wildly, but they’re talking about the same topic. Cosine similarity focuses on the overlapping keywords and themes rather than total word count, making it perfect for identifying that both are indeed about, say, “new product launches.”

Illustration for Cosine Similarity

        (Vector A)
           ↑
           |
(angle θ)   |          ← Both vectors share a strong directional similarity!
           |
           ↓
        (Vector B)

2. Dot Product

Dot product measures a combination of direction and magnitude. If you multiply the lengths of two vectors and the cosine of the angle between them, you get the dot product. This means if your vectors are large and align closely, you get a higher dot product value.

When to Use Dot Product

Weighted Matches: If the magnitude (length of the embedding) is significant—maybe you really do care that one document is larger or has higher “importance” in some feature dimension.
Neural Network Outputs: Often used in final layers or attention mechanisms where magnitude of embeddings is deliberately scaled or normalized in certain ways.

Dot Product Example

Picture a scenario where each vector encodes not just the direction (topic) but also how frequently that topic is discussed in the content. A bigger vector might mean the topic is covered more in-depth. If both vectors are huge and point in roughly the same direction, the dot product will be very large—great for capturing that strong alignment in both topic and quantity.

Illustration for Dot Product

  [Vector A: Magnitude = |A|]
         ↓
    (A) ----------·
                  \
                   \  High overlap means big dot product!
                  /
    (B) ----------·
         ↑
  [Vector B: Magnitude = |B|]

3. Euclidean Distance

Euclidean distance is the straight-line distance between two points in a multi-dimensional space—just like a ruler in geometry class. If you imagine each vector as a point on a graph, Euclidean tells you exactly how far one point is from the other.

When to Use Euclidean Distance

Spatial/Geometric Concepts: When your data naturally fits a scenario where direct distance matters. Think of a GPS coordinate system, or an image pixel comparison.
Clustering: Many clustering algorithms (like k-means) rely on Euclidean distance to group similar data points together.

Euclidean Distance Example

Consider you’re clustering customer preferences in a 2D space: one axis is “preferred price range,” and the other is “interest in premium features.” If two customers fall close to each other in this coordinate system, Euclidean distance will confirm they’re likely to have similar preferences.

Illustration for Euclidean Distance

        (Customer A)  •
                       \
                        \
          Distance d?    \
                          •  (Customer B)

Making Your Choice

Cosine Similarity
- Great for text or any scenario where direction matters more than magnitude.
- “We care about how similar the themes or angles are, ignoring length.”
Dot Product
- Useful when magnitude is also crucial.
- “Two large vectors that point in the same direction should rank higher than two small ones.”
Euclidean Distance
- Ideal for geometric-style problems or clustering.
- “We want to know how far apart two points are, literally, in multidimensional space.”

Summary

Choosing the right similarity measure depends on your use case. If you’re dealing with text embeddings and want to isolate direction over magnitude, go with Cosine Similarity. When overall vector size or weighting matters, Dot Product shines. And if your model benefits from real geometric distances—like clustering points in space—Euclidean Distance is the way to go.