matrixfactorization
Matrix factorization refers to a family of techniques for decomposing a matrix into the product of two or more smaller matrices. The canonical form seeks a low-rank approximation M ≈ U V^T, where M is an m×n matrix and U is m×k, V is n×k with k < min(m,n). This yields latent factors that can reveal structure in the data. Classic examples include singular value decomposition (SVD), which decomposes M into U Σ V^T with orthogonality constraints; and non-negative matrix factorization (NMF), which adds non-negativity constraints to produce interpretable factors.
Probabilistic and optimization-based variants, such as probabilistic matrix factorization (PMF), Bayesian PMF, and collaborative filtering approaches,
Applications span recommender systems, data compression, topic modeling, and computer vision. Limitations include the need to