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positive matrix factorization
Positive matrix factorization is a multivariate data analysis and dimensionality reduction method that decomposes a data matrix into the product of two lower-rank factor matrices constrained to contain non-negative values. By enforcing non-negativity, the technique represents the original data as purely additive combinations of underlying latent components, avoiding negative coefficients and yielding physically meaningful and interpretable features. The method commonly incorporates point-by-point measurement uncertainties into a weighted least-squares optimization framework, making it widely used across machine learning, chemometrics, and environmental science for tasks such as latent feature extraction and source apportionment.
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