A comparison of positive matrix factorization and the weighted multivariate curve resolution method. Application to environmental data

In recent years, positive matrix factorization, PMF, has gained popularity in environmental sciences and it has been recommended by the U.S. Environmental Protection Agency as a general modeling tool in air quality control. Among the attractive features contributing to its popularity is that measurement uncertainty information can be incorporated into the PMF model, which allows the handling of missing measurements and data below the reporting limits. In addition, the solutions obtained from PMF obey constraints such as the non-negativity of the source compositions and source contributions of samples that make their interpretation physically meaningful. A less popular multivariate curve resolution method based on a weighted alternating least-squares algorithm, MCR-WALS, also incorporates the measurement error information and non-negativity constraints, which makes this method a potential tool when obtaining composition and contribution profiles of environmental data. Both methods use the same loss function, but they differ in the way the profiles are obtained. The goal of this study was to compare the performance of PMF with the performance of MCR-WALS for data sets simulated with different correlation and error structures. The results showed that the profiles extracted by both methods are virtually the same for data with different error structures.