Matrix factorization is a technique commonly used in recommender systems to predict users' preferences for items by uncovering hidden patterns within user-item interactions. The core idea is to transform the original user-item interaction matrix, which usually contains ratings or interactions, into two lower-dimensional matrices: one representing users and the other representing items. Each entry in these matrices corresponds to latent factors that capture underlying characteristics of the users and items, respectively. When these two matrices are multiplied together, they can recreate an approximation of the original interaction matrix, allowing for the prediction of unrated items based on observed data.
For example, imagine a scenario where users rate movies. The user-item matrix might include ratings from users for various movies, but many entries could be missing. By applying matrix factorization, we can generate two matrices—one for users and one for movies. Each user might be represented by factors like "likes action" or "prefers romantic comedies," while each movie can be defined by its own set of features like "genre" or "cast." When we multiply these matrices, we can estimate the missing ratings by calculating how closely a user's preferences align with a movie's characteristics.
Matrix factorization has become particularly popular in collaborative filtering systems because it helps address the sparsity of the data. In many real-world scenarios, interactions between users and items are limited, making it challenging to directly apply traditional techniques to predict preferences. By using techniques like Singular Value Decomposition (SVD) or Alternating Least Squares (ALS) within matrix factorization, we can effectively identify and leverage the latent relationships that exist between users and items, leading to improved recommendations that better match individual tastes. This methodology has been successfully implemented by various platforms, including Netflix and Spotify, to enhance user engagement and satisfaction.