The application of Positive Matrix Factorization (PMF) to eco-efficiency analysis.

A new method for weighting and aggregating eco-efficiency indicators is of the utmost importance, if researchers in the field are to provide simplified and physically meaningful information to policy makers. To date, there is still considerable debate over which weighting and aggregating methods to use in this context. We apply a new variant of factor analysis, Positive Matrix Factorization (PMF), to a simple eco-efficiency analysis case study. PMF constrains its solutions to be non-negative, providing two important advantages over traditional factor analysis (FA) or principal component analysis (PCA): the rotational ambiguity of the solution space is reduced, and all the results are guaranteed to be physically meaningful. We suggest that PMF is better choice than either FA or PCA for eco-efficiency indicators, especially when dealing with complex social-economic and environmental data.