Cosine similarity is a mathematical measure used in recommender systems to quantify how similar two entities (like users or items) are based on their vector representations. It calculates the cosine of the angle between two vectors in a multi-dimensional space, producing a value between -1 and 1. A value closer to 1 indicates high similarity, while values near 0 or -1 suggest dissimilarity or opposing trends. In practice, cosine similarity is particularly useful in collaborative filtering, a common recommendation approach where the system identifies patterns in user-item interactions (e.g., ratings, purchases) to suggest relevant content.
In user-based collaborative filtering, cosine similarity compares user preference vectors. For example, in a movie recommendation system, each user can be represented as a vector where each dimension corresponds to a movie, and the value reflects their rating (or interaction). If two users have similar rating patterns—even if their rating scales differ—their vectors will point in a similar direction, yielding a high cosine score. The system can then recommend movies liked by one user to the other. Similarly, in item-based collaborative filtering, items (e.g., products, articles) are compared. If two books are frequently purchased by the same users, their vectors in a user-purchase matrix will align closely, and cosine similarity will flag them as related. For instance, if users who buy “Machine Learning Basics” also often buy “Data Science Handbook,” the system might recommend one when the other is viewed.
A key advantage of cosine similarity is its focus on directional alignment rather than magnitude, making it robust to differences in scale. This is critical in sparse datasets common in recommendation scenarios, where most user-item interactions are missing (e.g., users rate only a few items). However, cosine similarity can struggle with low-overlap cases—if two users have few shared interactions, the score may be unreliable. Developers often address this by combining it with techniques like TF-IDF weighting (to downweight popular items) or hybrid models that blend collaborative filtering with content-based methods. Despite its limitations, cosine similarity remains a foundational tool for building scalable, interpretable recommendation logic.