Cosine similarity is a mathematical measure that calculates the similarity between two vectors by determining the cosine of the angle between them. It ranges from -1 (completely opposite directions) to 1 (identical direction), with 0 indicating orthogonality (no similarity). In practice, it’s often used with normalized vectors, where the result depends solely on the direction of the vectors, not their magnitude. For example, if two text embeddings (numerical representations of text) point in the same direction in a high-dimensional space, their cosine similarity will be close to 1, indicating they’re semantically similar. If they’re unrelated, the angle between them widens, reducing the cosine score.
In semantic search, cosine similarity is used to compare how closely the meaning of a query matches the meaning of documents or other text snippets. This works because modern natural language processing (NLP) models like BERT or sentence transformers convert text into dense vector embeddings, where semantically similar texts are positioned closer in the vector space. For instance, a search query like “healthy eating habits” would be converted into a vector, and the system would compute the cosine similarity between this vector and precomputed vectors for all stored documents. Documents about “nutrition tips” or “balanced diets” would have high cosine similarity scores, while those about “car maintenance” would score lower. By focusing on the angle between vectors, cosine similarity ignores differences in vector length, which is useful because text length (e.g., a short query vs. a long article) doesn’t inherently affect semantic relevance.
The key advantage of cosine similarity in semantic search is its efficiency and focus on semantic meaning over literal term matching. Unlike exact keyword searches, which fail to capture synonyms or related concepts (e.g., “car” vs. “vehicle”), cosine similarity handles this by comparing the overall context encoded in vectors. It’s also computationally lightweight compared to alternatives like Euclidean distance, especially when vectors are pre-normalized (reducing the calculation to a simple dot product). For example, a search engine using cosine similarity can quickly rank millions of documents by relevance without recalculating vector magnitudes during queries. This balance of accuracy and speed makes it a practical choice for real-world applications like recommendation systems, chatbots, or document retrieval, where understanding intent is critical.