Articles | Volume 9, issue 2
https://doi.org/10.5194/acp-9-497-2009
© Author(s) 2009. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/acp-9-497-2009
© Author(s) 2009. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
22 Jan 2009
Assessing positive matrix factorization model fit: a new method to estimate uncertainty and bias in factor contributions at the measurement time scale
J. G. Hemann
Department of Applied Mathematics, University of Colorado, Boulder, USA
G. L. Brinkman
Department of Mechanical Engineering, University of Colorado, Boulder, USA
S. J. Dutton
Department of Mechanical Engineering, University of Colorado, Boulder, USA
M. P. Hannigan
Department of Mechanical Engineering, University of Colorado, Boulder, USA
J. B. Milford
Department of Mechanical Engineering, University of Colorado, Boulder, USA
S. L. Miller
Department of Mechanical Engineering, University of Colorado, Boulder, USA
Viewed
Total article views: 5,910 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 01 Feb 2013, article published on 14 Feb 2008)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 2,131 | 3,562 | 217 | 5,910 | 204 | 217 |
- HTML: 2,131
- PDF: 3,562
- XML: 217
- Total: 5,910
- BibTeX: 204
- EndNote: 217
Total article views: 4,629 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 01 Feb 2013, article published on 22 Jan 2009)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 1,859 | 2,569 | 201 | 4,629 | 180 | 208 |
- HTML: 1,859
- PDF: 2,569
- XML: 201
- Total: 4,629
- BibTeX: 180
- EndNote: 208
Total article views: 1,281 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 01 Feb 2013, article published on 14 Feb 2008)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 272 | 993 | 16 | 1,281 | 24 | 9 |
- HTML: 272
- PDF: 993
- XML: 16
- Total: 1,281
- BibTeX: 24
- EndNote: 9
Cited
40 citations as recorded by crossref.
- Size-segregated analysis of PAHs in Urban air: Source apportionment and health risk assessment in an Urban canal-adjacent environment S. Pongpiachan et al. https://doi.org/10.1371/journal.pone.0320405
- Source identification and co-occurrence patterns of major elements in South China Sea sediments T. Li et al. https://doi.org/10.1016/j.margeo.2020.106285
- Oxidative potential and source apportionment of size-resolved particles from indoor environments: Dithiothreitol (DTT) consumption and ROS production K. Yao et al. https://doi.org/10.1016/j.atmosenv.2023.120060
- Water resources pollution associated with risks of heavy metals from Vatukoula Goldmine region, Fiji S. Kumar et al. https://doi.org/10.1016/j.jenvman.2021.112868
- PMF Source Contribution Uncertainty Estimation via Effective Variance Least Squares J. Chen et al. https://doi.org/10.1021/acsestair.5c00312
- Concentrations and source insights for trace elements in fine and coarse particulate matter N. Clements et al. https://doi.org/10.1016/j.atmosenv.2014.01.011
- Application of Multivariate Statistical Techniques and Water Quality Index for the Assessment of Water Quality and Apportionment of Pollution Sources in the Yeongsan River, South Korea M. Mamun & K. An https://doi.org/10.3390/ijerph18168268
- Transported smoke from crop residue burning as the major source of organic aerosol and health risks in northern Indian cities during post-monsoon Y. Hao et al. https://doi.org/10.1016/j.envint.2025.109583
- PM2.5source apportionment with organic markers in the Southeastern Aerosol Research and Characterization (SEARCH) study J. Watson et al. https://doi.org/10.1080/10962247.2015.1063551
- Source apportionment and source-to-sink transport of major and trace elements in coastal sediments: Combining positive matrix factorization and sediment trend analysis T. Li et al. https://doi.org/10.1016/j.scitotenv.2018.09.198
- Disturbance mechanisms of lacustrine organic carbon burial: Case study of Cuopu Lake, Southwest China Q. Jiang et al. https://doi.org/10.1016/j.scitotenv.2020.140615
- Characterization of organic nitrogen in aerosols at a forest site in the southern Appalachian Mountains X. Chen et al. https://doi.org/10.5194/acp-18-6829-2018
- Impact of source collinearity in simulated PM2.5 data on the PMF receptor model solution R. Habre et al. https://doi.org/10.1016/j.atmosenv.2011.09.034
- Water soluble organic aerosols in the Colorado Rocky Mountains, USA: composition, sources and optical properties M. Xie et al. https://doi.org/10.1038/srep39339
- Risks Assessment Associated with Different Sources of Metals in Abandoned Soil of Zhuxianzhuang Coal Mine, Huaibei Coalfield (Anhui, China) H. Fang et al. https://doi.org/10.1007/s00128-020-03069-4
- Quantifying Source Apportionment, Co-occurrence, and Ecotoxicological Risk of Metals from Upstream, Lower Midstream, and Downstream River Segments, Bangladesh A. Towfiqul Islam et al. https://doi.org/10.1002/etc.4814
- Synthetic data generation from a fine particulate matter PM2.5 experimental data seed and its use in PMF and APCA J. Flores-Aldape et al. https://doi.org/10.1016/j.nimb.2024.165599
- Application of time series and multivariate statistical models for water quality assessment and pollution source apportionment in an Urban River, New Jersey, USA O. Soetan et al. https://doi.org/10.1007/s11356-024-35330-2
- Source apportionment resolved by time of day for improved deconvolution of primary source contributions to air pollution S. Bhandari et al. https://doi.org/10.5194/amt-15-6051-2022
- Measurement report: Collocated speciation and potential mechanisms of gaseous adsorption for integrated filter-based sampling and analysis of water-soluble organic molecular markers in the atmosphere W. Feng et al. https://doi.org/10.5194/acp-25-16697-2025
- Light absorption of organic carbon and its sources at a southeastern U.S. location in summer M. Xie et al. https://doi.org/10.1016/j.envpol.2018.09.125
- Mixed response of trace element concentrations in fluvial sediments to a flash flood in a former mining area A. Weber & F. Lehmkuhl https://doi.org/10.1186/s12302-024-00926-5
- Interpretation of organic components from Positive Matrix Factorization of aerosol mass spectrometric data I. Ulbrich et al. https://doi.org/10.5194/acp-9-2891-2009
- Integrated machine learning and positive matrix factorization for the source-specific contamination and predictive risk assessment of potentially toxic elements in multi-land-use soils around an active coal mine Z. Bashir et al. https://doi.org/10.1039/D5RA09789D
- Positive Matrix Factorization of PM2.5: Comparison and Implications of Using Different Speciation Data Sets M. Xie et al. https://doi.org/10.1021/es302358g
- Positive matrix factorization of PM2.5 – eliminating the effects of gas/particle partitioning of semivolatile organic compounds M. Xie et al. https://doi.org/10.5194/acp-13-7381-2013
- Development and evaluation of an integrated method using distance- and probability-based profile matching approaches in receptor modeling H. Liao et al. https://doi.org/10.1016/j.apr.2022.101423
- Oxidative potential induced by metal-organic interaction from PM2.5 in simulated biological fluids N. Wu et al. https://doi.org/10.1016/j.scitotenv.2022.157768
- Hazard ranking of wastewater sources in a highly polluted river in northern Taiwan by using positive matrix factorization with metal elements P. Hsieh et al. https://doi.org/10.1186/s42834-022-00144-9
- Impact of Gas/Particle Partitioning of Semivolatile Organic Compounds on Source Apportionment with Positive Matrix Factorization M. Xie et al. https://doi.org/10.1021/es5022262
- Characteristics and source apportionment of VOCs in the suburban area of Beijing, China G. Wang et al. https://doi.org/10.1016/j.apr.2016.03.006
- Measuring progress towards sustainable intensification: How far can secondary data go? A. Barnes & S. Thomson https://doi.org/10.1016/j.ecolind.2013.07.001
- Source apportionment using receptor model based on aerosol mass spectra and 1 h resolution chemical dataset in Tianjin, China X. Peng et al. https://doi.org/10.1016/j.atmosenv.2018.11.018
- Positive matrix factorization of a 32-month series of daily PM2.5 speciation data with incorporation of temperature stratification M. Xie et al. https://doi.org/10.1016/j.atmosenv.2012.09.034
- Integration of positive matrix factorization and water quality models for pollution source identification and water quality enhancement in rivers S. Kim https://doi.org/10.1007/s13201-025-02393-6
- Quantitative source apportionment of heavy metals in cultivated soil and associated model uncertainty L. Chai et al. https://doi.org/10.1016/j.ecoenv.2021.112150
- Intra-urban spatial variability and uncertainty assessment of PM2.5 sources based on carbonaceous species M. Xie et al. https://doi.org/10.1016/j.atmosenv.2012.06.036
- Application of machine learning in atmospheric pollution research: A state-of-art review Z. Peng et al. https://doi.org/10.1016/j.scitotenv.2023.168588
- Identification of pollution sources in rivers by downstream analysis of low-concentration elements associated with wastewater H. Lin et al. https://doi.org/10.1007/s13762-024-05539-2
- Uncertainty in positive matrix factorization solutions for PAHs in surface sediments of the Yangtze River Estuary in different seasons R. Liu et al. https://doi.org/10.1016/j.chemosphere.2017.10.070
40 citations as recorded by crossref.
- Size-segregated analysis of PAHs in Urban air: Source apportionment and health risk assessment in an Urban canal-adjacent environment S. Pongpiachan et al. https://doi.org/10.1371/journal.pone.0320405
- Source identification and co-occurrence patterns of major elements in South China Sea sediments T. Li et al. https://doi.org/10.1016/j.margeo.2020.106285
- Oxidative potential and source apportionment of size-resolved particles from indoor environments: Dithiothreitol (DTT) consumption and ROS production K. Yao et al. https://doi.org/10.1016/j.atmosenv.2023.120060
- Water resources pollution associated with risks of heavy metals from Vatukoula Goldmine region, Fiji S. Kumar et al. https://doi.org/10.1016/j.jenvman.2021.112868
- PMF Source Contribution Uncertainty Estimation via Effective Variance Least Squares J. Chen et al. https://doi.org/10.1021/acsestair.5c00312
- Concentrations and source insights for trace elements in fine and coarse particulate matter N. Clements et al. https://doi.org/10.1016/j.atmosenv.2014.01.011
- Application of Multivariate Statistical Techniques and Water Quality Index for the Assessment of Water Quality and Apportionment of Pollution Sources in the Yeongsan River, South Korea M. Mamun & K. An https://doi.org/10.3390/ijerph18168268
- Transported smoke from crop residue burning as the major source of organic aerosol and health risks in northern Indian cities during post-monsoon Y. Hao et al. https://doi.org/10.1016/j.envint.2025.109583
- PM2.5source apportionment with organic markers in the Southeastern Aerosol Research and Characterization (SEARCH) study J. Watson et al. https://doi.org/10.1080/10962247.2015.1063551
- Source apportionment and source-to-sink transport of major and trace elements in coastal sediments: Combining positive matrix factorization and sediment trend analysis T. Li et al. https://doi.org/10.1016/j.scitotenv.2018.09.198
- Disturbance mechanisms of lacustrine organic carbon burial: Case study of Cuopu Lake, Southwest China Q. Jiang et al. https://doi.org/10.1016/j.scitotenv.2020.140615
- Characterization of organic nitrogen in aerosols at a forest site in the southern Appalachian Mountains X. Chen et al. https://doi.org/10.5194/acp-18-6829-2018
- Impact of source collinearity in simulated PM2.5 data on the PMF receptor model solution R. Habre et al. https://doi.org/10.1016/j.atmosenv.2011.09.034
- Water soluble organic aerosols in the Colorado Rocky Mountains, USA: composition, sources and optical properties M. Xie et al. https://doi.org/10.1038/srep39339
- Risks Assessment Associated with Different Sources of Metals in Abandoned Soil of Zhuxianzhuang Coal Mine, Huaibei Coalfield (Anhui, China) H. Fang et al. https://doi.org/10.1007/s00128-020-03069-4
- Quantifying Source Apportionment, Co-occurrence, and Ecotoxicological Risk of Metals from Upstream, Lower Midstream, and Downstream River Segments, Bangladesh A. Towfiqul Islam et al. https://doi.org/10.1002/etc.4814
- Synthetic data generation from a fine particulate matter PM2.5 experimental data seed and its use in PMF and APCA J. Flores-Aldape et al. https://doi.org/10.1016/j.nimb.2024.165599
- Application of time series and multivariate statistical models for water quality assessment and pollution source apportionment in an Urban River, New Jersey, USA O. Soetan et al. https://doi.org/10.1007/s11356-024-35330-2
- Source apportionment resolved by time of day for improved deconvolution of primary source contributions to air pollution S. Bhandari et al. https://doi.org/10.5194/amt-15-6051-2022
- Measurement report: Collocated speciation and potential mechanisms of gaseous adsorption for integrated filter-based sampling and analysis of water-soluble organic molecular markers in the atmosphere W. Feng et al. https://doi.org/10.5194/acp-25-16697-2025
- Light absorption of organic carbon and its sources at a southeastern U.S. location in summer M. Xie et al. https://doi.org/10.1016/j.envpol.2018.09.125
- Mixed response of trace element concentrations in fluvial sediments to a flash flood in a former mining area A. Weber & F. Lehmkuhl https://doi.org/10.1186/s12302-024-00926-5
- Interpretation of organic components from Positive Matrix Factorization of aerosol mass spectrometric data I. Ulbrich et al. https://doi.org/10.5194/acp-9-2891-2009
- Integrated machine learning and positive matrix factorization for the source-specific contamination and predictive risk assessment of potentially toxic elements in multi-land-use soils around an active coal mine Z. Bashir et al. https://doi.org/10.1039/D5RA09789D
- Positive Matrix Factorization of PM2.5: Comparison and Implications of Using Different Speciation Data Sets M. Xie et al. https://doi.org/10.1021/es302358g
- Positive matrix factorization of PM2.5 – eliminating the effects of gas/particle partitioning of semivolatile organic compounds M. Xie et al. https://doi.org/10.5194/acp-13-7381-2013
- Development and evaluation of an integrated method using distance- and probability-based profile matching approaches in receptor modeling H. Liao et al. https://doi.org/10.1016/j.apr.2022.101423
- Oxidative potential induced by metal-organic interaction from PM2.5 in simulated biological fluids N. Wu et al. https://doi.org/10.1016/j.scitotenv.2022.157768
- Hazard ranking of wastewater sources in a highly polluted river in northern Taiwan by using positive matrix factorization with metal elements P. Hsieh et al. https://doi.org/10.1186/s42834-022-00144-9
- Impact of Gas/Particle Partitioning of Semivolatile Organic Compounds on Source Apportionment with Positive Matrix Factorization M. Xie et al. https://doi.org/10.1021/es5022262
- Characteristics and source apportionment of VOCs in the suburban area of Beijing, China G. Wang et al. https://doi.org/10.1016/j.apr.2016.03.006
- Measuring progress towards sustainable intensification: How far can secondary data go? A. Barnes & S. Thomson https://doi.org/10.1016/j.ecolind.2013.07.001
- Source apportionment using receptor model based on aerosol mass spectra and 1 h resolution chemical dataset in Tianjin, China X. Peng et al. https://doi.org/10.1016/j.atmosenv.2018.11.018
- Positive matrix factorization of a 32-month series of daily PM2.5 speciation data with incorporation of temperature stratification M. Xie et al. https://doi.org/10.1016/j.atmosenv.2012.09.034
- Integration of positive matrix factorization and water quality models for pollution source identification and water quality enhancement in rivers S. Kim https://doi.org/10.1007/s13201-025-02393-6
- Quantitative source apportionment of heavy metals in cultivated soil and associated model uncertainty L. Chai et al. https://doi.org/10.1016/j.ecoenv.2021.112150
- Intra-urban spatial variability and uncertainty assessment of PM2.5 sources based on carbonaceous species M. Xie et al. https://doi.org/10.1016/j.atmosenv.2012.06.036
- Application of machine learning in atmospheric pollution research: A state-of-art review Z. Peng et al. https://doi.org/10.1016/j.scitotenv.2023.168588
- Identification of pollution sources in rivers by downstream analysis of low-concentration elements associated with wastewater H. Lin et al. https://doi.org/10.1007/s13762-024-05539-2
- Uncertainty in positive matrix factorization solutions for PAHs in surface sediments of the Yangtze River Estuary in different seasons R. Liu et al. https://doi.org/10.1016/j.chemosphere.2017.10.070
Saved (final revised paper)
Latest update: 18 Jul 2026
Altmetrics
Final-revised paper
Preprint