Truncated SVD is a matrix factorization technique that reduces data dimensionality by decomposing a matrix into U, Σ, and V components, then zeroing out smaller singular values to reconstruct an approximation. Applied to a 1024×1024 moon image, keeping just 32 of 1024 components achieves 16x data reduction while preserving recognizable image quality, demonstrating how leading components capture most information.
Recommendation systems have evolved from collaborative filtering methods that identify similar users or items based on past interactions, to latent factor models using matrix factorization that represent items and users as vectors in a factor space to overcome sparsity and similarity limitations.