# Positive Matrix Factorization

## Positive matrix factorization (PMF) was developed by Dr. P. Paatero (Dept. of Physics, University of Helsinki). PMF can be used to determine source profiles based on the ambient data. Features include the following:

- PMF uses weighted least squares fits for data that are normally distributed and maximum likelihood estimates for data that are distributed long normally.
- PMF weights data points by their analytical uncertainties.
- PMF constrains factor loadings and factor scores to nonnegative values and thereby minimizes the ambiguity caused by rotating factors. This is one of the major differences between PMF and principal component analysis (PCA).
- PMF expresses factor loadings in mass units which allows factors to be used directly as source signatures.
- PMF provides uncertainties for factor loadings and factor scores which makes the loadings and scores easier to use in quantitative procedures such as chemical mass balance.