Characteristic pattern analysis of polybromodiphenyl ethers in Great Lakes sediments: a combination of eigenspace projection and positive matrix factorization analysis

Anew idea in receptormodeling is proposed, which utilizes a geometric eigenspace projection combinedwith amild alternative matrix updating technique. The eigenspace projection determines the sources or characteristic patterns as vertices that can span all measurements in a multidimensional eigenspace. The mild alternative matrix updating algorithm refines the results determined by the eigenspace projection to generate the optimized source profiles. Positive matrix factorization (PMF) analysis was adopted to suggest initial characteristic patterns. The advantage of the eigenspace projection method, compared with a purely computational matrix updating method, is that it can substantially avoid rotational ambiguity. The matrix refining step can effectively minimize data uncertainties. The application of this method has been illustrated step by step through a case study on determination of polybromodiphenyl ether (PBDE) characteristic congener patterns in the sediments of the Laurentian Great Lakes of North America. The number of factors was determined to be five for the Great Lakes PBDE 2002 data set. The sum of squares of error and coefficient of determination (r) suggested that the results obtained using this method are better than those from three known sources or the initial application of PMF. The factors represent deca (Saytex 102E), penta (DE-71), and octa (DE-79) technical PBDE mixtures as sources and two degradation factors that may have been generated by both photolysis and biological debromination. Copyright © 2012 John Wiley & Sons, Ltd. Supporting information may be found in the online version of this paper.