Matrix factorization is a core technique in recommendation systems and collaborative filtering, with Singular Value Decomposition (SVD) and Alternating Least Squares (ALS) being two widely used methods. These approaches decompose a user-item interaction matrix (e.g., movie ratings) into lower-dimensional latent factor matrices that capture underlying patterns. SVD and ALS differ in their mathematical foundations and optimization strategies, making them suitable for different scenarios.
SVD is a linear algebra technique that factorizes a matrix into three components: user factors, singular values, and item factors. In recommendation systems, truncated SVD is often applied to approximate the original matrix by retaining only the top latent features (e.g., 50-100 factors). For example, a movie rating matrix with users as rows and movies as columns can be decomposed into user preferences and movie attributes. However, traditional SVD struggles with missing data (common in real-world datasets) and computational complexity. To address this, methods like FunkSVD (popularized during the Netflix Prize) optimize the factorization using gradient descent, focusing only on observed entries. Libraries like Surprise or SciKit-Learn provide implementations for such cases.
ALS, on the other hand, is an optimization approach specifically designed for handling sparse data and scalability. It alternately fixes one set of latent factors (user or item) and solves for the other using least squares regression. For instance, ALS might first update user factors while keeping item factors fixed, then reverse the process, iterating until convergence. This method works well with implicit feedback (e.g., clicks or view counts) and allows for regularization to prevent overfitting. Apache Spark’s MLlib includes an ALS implementation optimized for distributed computing, making it practical for large datasets. ALS is particularly effective when parallelization is needed, as user and item updates can be computed independently.
In practice, SVD-based methods are often preferred for smaller, dense datasets where interpretability of latent factors matters, while ALS excels in scalability and handling sparse, implicit data. Developers should consider data size, sparsity, and the need for parallel processing when choosing between them. Both techniques remain foundational in building recommendation systems, with trade-offs balancing computational efficiency and accuracy.