What is matrix factorization in recommender systems?

Matrix factorization is a core technique in recommender systems that helps predict user preferences by breaking down large, sparse datasets into more manageable components. At its core, it models interactions between users and items (e.g., movies, products) by representing them as latent features in a lower-dimensional space. This approach transforms the problem of predicting missing user-item ratings (like a movie a user hasn’t watched) into a mathematical optimization task, making it efficient for large-scale datasets.

The process starts with a user-item interaction matrix, where rows represent users, columns represent items, and entries contain ratings or implicit feedback (e.g., clicks). Since most users interact with only a small subset of items, this matrix is typically sparse. Matrix factorization decomposes this matrix into two smaller matrices: a user matrix and an item matrix. Each user is represented by a vector of latent features (e.g., preferences for genres in movies), and each item is represented by a vector of latent attributes (e.g., movie genre traits). The dot product of a user’s vector and an item’s vector approximates the user’s predicted rating for that item. For example, if a user vector has high values for “action” and “adventure,” and a movie vector has similar high values, their dot product will predict a strong preference.

To train the model, algorithms like stochastic gradient descent (SGD) or alternating least squares (ALS) minimize the error between predicted and actual ratings while applying regularization to avoid overfitting. For instance, in a movie recommendation system, the model might learn that User A prefers vectors aligned with “sci-fi” and “drama,” while Movie X has vectors for “sci-fi” and “action.” Even if User A hasn’t rated Movie X, the model infers a likely high rating based on overlapping features. This method scales well, handles sparsity effectively, and allows for efficient updates as new data arrives. By capturing hidden patterns, matrix factorization provides a robust framework for personalized recommendations, forming the backbone of many production systems.