How is similarity measured in vector search?

Similarity in vector search is measured using mathematical techniques that compare the “distance” or angle between vectors in a multi-dimensional space. The core idea is that vectors representing similar items (like text, images, or user preferences) will be closer to each other in this space. Common methods include cosine similarity, Euclidean distance, and dot product calculations. These techniques quantify how alike two vectors are, enabling systems to rank results by relevance. For example, in a search engine, vectors representing documents are compared to a query vector, and the closest matches are returned.

The most widely used metric is cosine similarity, which measures the angle between two vectors, ignoring their magnitudes. This is particularly useful when the direction of the vector matters more than its length, such as in text embeddings where word frequency or TF-IDF values create sparse, high-dimensional vectors. For instance, if two news articles have vectors pointing in similar directions (even if one is longer due to more text), cosine similarity will still detect topical similarity. Another method is Euclidean distance (L2 distance), which calculates the straight-line distance between vectors in space. This works well when both direction and magnitude are important, like in image embeddings where pixel intensity differences matter. A third approach is the dot product, which combines vector magnitudes and their angular relationship. When vectors are normalized (unit length), the dot product becomes equivalent to cosine similarity. For example, recommendation systems often use dot products to weigh both user preference strength (magnitude) and item alignment (direction).

The choice of metric depends on the data and application. Cosine similarity is efficient for sparse, high-dimensional data (e.g., text), while Euclidean distance suits dense, low-dimensional data (e.g., images). Practical implementation often involves trade-offs: cosine similarity avoids magnitude bias but may require normalization, while Euclidean distance can be computationally heavier for large datasets. Libraries like FAISS or Annoy optimize these calculations for speed. For example, a music streaming service might use cosine similarity to recommend songs based on genre (direction) but switch to Euclidean distance if tempo (magnitude) is critical. Understanding these nuances ensures developers select the right tool for accurate, efficient search.