Cosine similarity is a measure used in vector search to determine how similar two vectors are by calculating the cosine of the angle between them. Mathematically, it computes the dot product of the vectors divided by the product of their magnitudes. The result ranges from -1 (opposite directions) to 1 (identical direction), with 0 indicating orthogonality. Unlike distance-based metrics, it focuses on orientation rather than magnitude, making it useful for comparing vectors in high-dimensional spaces where relative direction matters more than absolute position. For example, in natural language processing, word embeddings (like those from Word2Vec) represent words as vectors, and cosine similarity helps identify semantically related words by measuring their directional alignment.
In vector search, cosine similarity is often preferred over metrics like Euclidean distance because it effectively handles differences in vector scale. For instance, in document retrieval, a text document might be represented as a TF-IDF vector where each dimension corresponds to a word’s importance. Two documents on the same topic could have vastly different lengths (and thus vector magnitudes), but their vectors would point in a similar direction. Cosine similarity ignores the magnitude difference and focuses on the shared thematic content. This property makes it ideal for applications like recommendation systems, where the goal is to find items with similar characteristics, not necessarily items of the same “size” or intensity. Vector databases often optimize for cosine similarity by normalizing vectors to unit length, which simplifies the calculation to a dot product, improving computational efficiency.
A practical example of cosine similarity in action is image search. Suppose an image is encoded into a feature vector using a convolutional neural network (CNN). When a user queries with an image, the system computes the cosine similarity between the query vector and all stored image vectors to find the closest matches. Similarly, in semantic text search, embeddings from models like BERT are compared using cosine similarity to retrieve documents with similar meanings. One key consideration is preprocessing: vectors must be normalized (scaled to unit length) to ensure accurate results. For developers, libraries like NumPy or frameworks like Faiss provide built-in functions to compute cosine similarity efficiently. By leveraging directional alignment, cosine similarity offers a robust way to measure similarity in scenarios where magnitude is irrelevant or noisy.