Duality in multivariate receptor models

Multivariate receptor models are used for source apportionment of multiple observations of compositional data of air pollutants that obey mass conservation. Singular value decomposition of the data leads to two sets of eigenvectors. One set of eigenvectors spans a space in which source compositions are points and source contributions are hyperplanes. This space is shown to be dual to the space spanned by the second set of eigenvectors of the data in which source compositions are hyperplanes and source contributions are points. The analytical formulae for this duality are given. Finally, the duality principle is applied to greatly increase the computational speed of the Unmix multivariate receptor model.