Non-Negative Matrix Factorization

Non-negative matrix factorization represents data as a product of nonnegative factors, making components additive and often easier to interpret as topics, sources, communities, or biological signals. Researchers develop multiplicative updates, alternating least-squares and gradient methods, and structured variants that incorporate sparsity, graphs, temporal variation, or suitable count-data noise models. Applications include topic modeling, spectral unmixing, audio separation, clustering, and analysis of biological and network data. A central challenge is that factors may not be uniquely identifiable, especially with noisy or highly mixed observations, so work balances stronger recovery guarantees and useful structure against computational cost and assumptions that may not fit the data.