The accuracy of two- and three-way positive matrix factorization models: Applying simulated multisite data sets

References

• Abdollahi, H., and S.M. Sajjadi. 2010. On rotational ambiguity in parallel factor analysis. Chemom. Intell. Lab. Syst. 103:144–51. doi:10.1016/j.chemolab.2010.06.010
   Web of Science ®Google Scholar
• Belsley, D.A., E. Kuh, and R.E. Welsch. 2005. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York, NY: John Wiley & Sons.
   Google Scholar
• Beuck, H., U. Quass, O. Klemm, and T.A.J. Kuhlbusch. 2011. Assessment of sea salt and mineral dust contributions to PM10 in NW Germany using tracer models and positive matrix factorization. Atmos. Environ. 45:5813–21. doi:10.1016/j.atmosenv.2011.07.010
   Web of Science ®Google Scholar
• Brinkman, G., G. Vance, M.P. Hannigan, and J.B. Milford. 2006. Use of synthetic data to evaluate positive matrix factorization as a source apportionment tool for PM2.5 exposure data. Environ. Sci. Technol. 40:1892–901. doi:10.1021/es051712y
   PubMed Web of Science ®Google Scholar
• Bruinen de Bruin, Y., K. Koistinen, T. Yli-Tuomi, S. Kephalopoulos, and M. Jantunen. 2006. Source apportionment techniques and marker substances available for identification of personal exposure, indoor and outdoor sources of chemicals. EUR 22349 EN, Joint Research Center JRC, Ispra, Italy. ISBN 92-79-02981-9.
   Google Scholar
• Chan, Y.C., O. Hawas, D. Hawker, P. Vowles, D.D. Cohen, E. Stelcer, R. Simpson, G. Golding, and E. Christensen. 2011. Using multiple type composition data and wind data in PMF analysis to apportion and locate sources of air pollutants. Atmos. Environ. 45:439–49. doi:10.1016/j.atmosenv.2010.09.060
   Web of Science ®Google Scholar
• Chen, L.W.A., D.H. Lowenthal, J.G. Watson, D. Koracin, N. Kumar, E.M. Knipping, N. Wheeler, K. Craig, and S. Reid. 2010. Toward effective source apportionment using positive matrix factorization: Experiments with simulated PM2.5 data. J. Air Waste Manage Assoc. 60:43–54. doi:10.3155/1047-3289.60.1.43
   PubMed Web of Science ®Google Scholar
• Escrig, A., E. Monfort, I. Celades, X. Querol, F. Amato, M.C. Minguillón, and P.K. Hopke. 2009. Application of optimally scaled target factor analysis for assessing source contribution of ambient PM10. J. Air Waste Manage Assoc. 59:1296–307. doi:10.3155/1047-3289.59.11.1296
   Web of Science ®Google Scholar
• Faber, N.M., R. Bro, and P.K. Hopke. 2003. Recent developments in CANDECOMP/PARAFAC algorithms: A critical review. Chemom. Intell. Lab. Syst. 65:119–37. doi:10.1016/S0169-7439(02)00089-8
   Web of Science ®Google Scholar
• Green, M.C., L.W.A. Chen, D.W. DuBois, and J.V. Molenar. 2012. Fine particulate matter and visibility in the Lake Tahoe Basin: Chemical characterization, trends, and source apportionment. J. Air Waste Manage Assoc. 62: 53–65. doi:10.1080/10962247.2012.690362
   Web of Science ®Google Scholar
• Gu, J., J. Schnelle-Kreis, M. Pitz, J. Diemer, A. Reller, R. Zimmermann, J. Soentgen, A. Peters, and J. Cyrys. 2013. Spatial and temporal variability of PM10 sources in Augsburg, Germany. Atmos. Environ. 71:131–39. doi:10.1016/j.atmosenv.2013.01.043
   Web of Science ®Google Scholar
• Habre, R., B. Coull, and P. Koutrakis. 2011. Impact of source collinearity in simulated PM2.5 data on the PMF receptor model solution. Atmos. Environ. 45:6938–46. doi:10.1016/j.atmosenv.2011.09.034
   Web of Science ®Google Scholar
• Henry, R.C., and E.R. Christensen. 2010. Selecting an appropriate multivariate source apportionment model result. Environ. Sci. Technol. 44: 2474–2481. doi:10.1021/es9018095
   PubMed Web of Science ®Google Scholar
• Hwang, I., P.K. Hopke, and J.P. Pinto. 2008. Source apportionment and spatial distributions of coarse particles during the regional air pollution study. Environ. Sci. Technol. 42:3524–30. doi:10.1021/es0716204
   PubMed Web of Science ®Google Scholar
• Javitz, H.S., J.G. Watson, and N. Robinson. 1988. Performance of the chemical mass balance model with simulated local-scale aerosol. Atmos. Environ. 22:2309–22. doi:10.1016/0004-6981(88)90142-4
   Web of Science ®Google Scholar
• Kelly, K.E., R. Kotchenruther, R. Kuprov, and G.D. Silcox. 2013. Receptor model source attributions for Utah’s Salt Lake City airshed and the impacts of wintertime secondary ammonium nitrate and ammonium chloride aerosol. J. Air Waste Manage Assoc. 63:575–90. doi:10.1080/10962247.2013.774819
   Web of Science ®Google Scholar
• Keuken, M.P., M. Moerman, M. Voogt, M. Blom, E.P. Weijers, T. Röckmann, and U. Dusek. 2013. Source contributions to PM2.5 and PM10 at an urban background and a street location. Atmos. Environ. 71:26–35. doi:10.1016/j.atmosenv.2013.01.032
   Web of Science ®Google Scholar
• Kim, E., P.K. Hopke, J.P. Pinto, and W. Wilson. 2005. Spatial variability of fine particle mass, components, and source contributions during the regional air pollution study in St. Louis. Environ. Sci. Technol. 39:4172–79. doi:10.1021/es049824x
   PubMed Web of Science ®Google Scholar
• Larsen, B.R., S. Gilardoni, K. Stenström, J. Niedzialek, J. Jimenez, and C.A. Belis. 2012. Sources for PM air pollution in the Po Plain, Italy: II. Probabilistic uncertainty characterization and sensitivity analysis of secondary and primary sources. Atmos. Environ. 50:203–13. doi:10.1016/j.atmosenv.2011.12.038
   Web of Science ®Google Scholar
• Lowenthal, D.H., J.G. Watson, D. Koracin, L.W.A. Chen, D. Dubois, R. Vellore, N. Kumar, E.M. Kumar, N. Wheeler, and K. Craig. 2012. Evaluation of regional-scale receptor modeling. J. Air Waste Manage Assoc. 60:26–42. doi:10.3155/1047-3289.60.1.26
   Web of Science ®Google Scholar
• Marmur, A., A. Unal, J.A. Mulholland, and A.G. Russell. 2005. Optimization-based source apportionment of PM2.5 incorporating gas-to-particle ratios. Environ. Sci. Technol. 39:3245–54. doi:10.1021/es0490121
   PubMed Web of Science ®Google Scholar
• Minguillón, M.C., X. Querol, U. Baltensperger, and A.S.H. Prévôt. 2012. Fine and coarse PM composition and sources in rural and urban sites in Switzerland: Local or regional pollution. Sci. Total Environ. 427–28: 191–202. doi:10.1016/j.scitotenv.2012.04.030
   PubMed Web of Science ®Google Scholar
• Mooibroek, D., M. Schaap, E.P. Weijers, and R. Hoogerbrugge. 2011. Source apportionment and spatial variability of PM2.5 using measurements at five sites in the Netherlands. Atmos. Environ. 45:4180–91. doi:10.1016/j.atmosenv.2011.05.017
   Web of Science ®Google Scholar
• Ofosu, F.G., P.K. Hopke, I.J.K. Aboh, and S.A. Bamford. 2013. Biomass burning contribution to ambient air particulate levels at Navrongo in the Savannah zone of Ghana. J. Air Waste Manage Assoc. 63:1036–45. doi:10.1080/10962247.2013.783888
   Web of Science ®Google Scholar
• Öztürk, F., A. Zararsız, V.A. Dutkiewicz, L. Husain, P.K. Hopke, and G. Tuncel. 2012. Temporal variations and sources of Eastern Mediterranean aerosols based on a 9-year observation. Atmos. Environ. 61:463–75. doi:10.1016/j.atmosenv.2012.07.051
   Web of Science ®Google Scholar
• Paatero, P., and U. Tapper. 1994. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5:111–26. doi:10.1002/(ISSN)1099-095X
   Web of Science ®Google Scholar
• Paatero, P. 1997. A weighted non-negative least squares algorithm for three-way “PARAFAC’ factor analysis. Chemom. Intell. Lab. Syst. 38:223–42. doi:10.1016/S0169-7439(97)00031-2
   Web of Science ®Google Scholar
• Paatero, P. 1999. The Multilinear Engine—A table-driven least squares program for solving multilinear problems, including the n-way parallel factor analysis model. J. Comput. Graph. Stat. 8:854–88. doi:10.2307/1390831
   Web of Science ®Google Scholar
• Paatero, P. 2007. User’s Guide for Positive Matrix Factorization Programs PMF2 and PMF3, Part 1–2: Tutorial. Helsinki, Finland: University of Helsinki.
   Google Scholar
• Pant, P., and R.M. Harrison. 2012. Critical review of receptor modelling for particulate matter: A case study of India. Atmos. Environ. 49:1–12. doi:10.1016/j.atmosenv.2011.11.060
   Web of Science ®Google Scholar
• Pokorna, P., J. Hovorka, J. Krouzek, and P.K. Hopke. 2013. Particulate matter source apportionment in a village situated in industrial region of Central Europe. J. Air Waste Manage Assoc. 63:1412–21. doi:10.1080/10962247.2013.825215
   Web of Science ®Google Scholar
• Russell, A.G., and B.A. Brunekreef. 2009. A focus on particulate matter and health. Environ. Sci. Technol. 43:4620–25. doi:10.1021/es9005459
   PubMed Web of Science ®Google Scholar
• Shen, G.F., S. Wei, W. Wei, Y. Zhang, Y. Min, B. Wang, R. Wang, W. Li, H. Shen, Y. Huang, Y. Yang, W. Wang, X. Wang, X. Wang, and S. Tao. 2012. Emission factors, size distributions, and emission inventories of carbonaceous particulate matter from residential wood combustion in rural China. Environ. Sci. Technol. 46:4207–14. doi:10.1021/es203957u
   PubMed Web of Science ®Google Scholar
• Shen, G.F., M. Xue, S.Y. Yuan, J. Zhang, Q.Y. Zaho, B. Li, H.S. Wu, and A.J. Ding. 2014. Chemical compositions and reconstructed light extinction coefficients of particulate matter in a mega-city in the western Yangtze River Delta, China. Atmos. Environ. 83:14–20. doi:10.1016/j.atmosenv.2013.10.055
   Web of Science ®Google Scholar
• Shi, G.L., X. Li, Y.C. Feng, Y.Q. Wang, J.H. Wu, J. Li, and T. Zhu. 2009a. Combined source apportionment, using positive matrix factorization-chemical mass balance and principal component analysis/multiple linear regression-chemical mass balance models. Atmos. Environ. 43:2929–37. doi:10.1016/j.atmosenv.2009.02.054
   Web of Science ®Google Scholar
• Shi, G.L., Y.C. Feng, G. Zeng, X. Li, Y.F. Zhang, Y.Q. Wang, and T. Zhu. 2009b. Use of a nonnegative constrained principal component regression chemical mass balance model to study the contributions of nearly collinear sources. Environ. Sci. Technol. 43:8867–73. doi:10.1021/es902785c
   PubMed Web of Science ®Google Scholar
• Shi, G.L., F. Zeng, X. Li, Y.C. Feng, Y.Q. Wang, G.X. Liu, and T. Zhu. 2011a. Estimated contributions and uncertainties of PCA/MLR-CMB results: Source apportionment for synthetic and ambient data sets. Atmos. Environ. 45:2811–19. doi:10.1016/j.atmosenv.2011.03.007
   Web of Science ®Google Scholar
• Shi, G.L., Y.Z. Tian, Y.F. Zhang, W.Y. Ye, X. Li, X.X. Tie, Y.C. Feng, and T. Zhu. 2011b. Estimation of the concentrations of primary and secondary organic carbon in ambient particulate matter: Application of the CMB-Iteration method. Atmos. Environ. 45:5692–98. doi:10.1016/j.atmosenv.2011.07.031
   Web of Science ®Google Scholar
• Titos, G., H. Lyamani, M. Pandolfi, A. Alastuey, and L. Alados-Arboledas. 2014. Identification of fine (PM1) and coarse (PM10-1) sources of particulate matter in an urban environment. Atmos. Environ. 89:593–602. doi:10.1016/j.atmosenv.2014.03.001
   Web of Science ®Google Scholar
• Watson, J.G., and J.C. Chow. 2001. Source characterization of major emission sources in the Imperial and Mexicali Valleys along the US–Mexico border. Sci. Total Environ. 276:33–47. doi:10.1016/S0048-9697(01)00770-7
   PubMed Web of Science ®Google Scholar
• Watson, J.G., L.W. Antony Chen, J.C. Chow, P. Doraiswamy, and D.H. Lowenthal. 2008. Source apportionment: Findings from the U.S. Supersites program. J. Air Waste Manage Assoc. 58:265–88. doi:10.3155/1047-3289.58.2.265
   Web of Science ®Google Scholar
• Xie, M., T.L. Coons, J.G. Hemann, S.J. Dutton, J.B. Milford, J.L. Peel, S.L. Miller, S.Y. Kim, S. Vedal, L. Sheppard, and M.P. Hannigan. 2012. Intra-urban spatial variability and uncertainty assessment of PM2.5 sources based on carbonaceous species. Atmos. Environ. 60:305–15. doi:10.1016/j.atmosenv.2012.06.036
   Web of Science ®Google Scholar
• Zeng, Y.S., and P.K. Hopke. 1992. A new receptor model: A direct trilinear decomposition followed by a matrix reconstruction. J. Chemom. 6:65–83. doi:10.1002/(ISSN)1099-128X
   Web of Science ®Google Scholar
• Zhao, X.J., P.S. Zhao, J. Xu, W. Meng, W.W. Pu, F. Dong, D. He, and Q.F. Shi. 2013a. Analysis of a winter regional haze event and its formation mechanism in the North China Plain. Atmos. Chem. Phys. 13:5685–96. doi:10.5194/acp-13-5685-2013
   Web of Science ®Google Scholar
• Zhao, P.S., F. Dong, Y.D. Yang, D. He, X.J. Zhao, W.Z. Zhamng, Q. Yao, and H.Y. Liu. 2013b. Characteristics of carbonaceous aerosol in the region of Beijing, Tianjin, and Hebei, China. Atmos. Environ. 71:389–98. doi:10.1016/j.atmosenv.2013.02.010
   Web of Science ®Google Scholar
• Zheng, M., G.R. Cass, L. Ke, F. Wang, J.J. Schauer, E.S. Edgerton, and A.G. Russell. 2007. Source apportionment of daily fine particulate matter at Jefferson Street, Atlanta, GA, during summer and winter. J. Air Waste Manage Assoc. 57:228–42. doi:10.1080/10473289.2007.10465322
   Web of Science ®Google Scholar
• Zheng, M., F. Wang, G.S.W. Hagler, X. Hou, M. Bergin, Y. Cheng, L.G. Salmon, J.J. Schauer, P.K.K. Louie, L. Zeng, and Y.H. Zhang. 2011. Sources of excess urban carbonaceous aerosol in the Pearl River Delta Region, China. Atmos. Environ. 45:1175–82. doi:10.1016/j.atmosenv.2010.09.041
   Web of Science ®Google Scholar