Determining the number of factors for non-negative matrix and its application in source apportionment of air pollution in Singapore

Yan, Ming; Yang, Xiaojie; Hang, Weiqiang; Xia, Yingcun

doi:10.1007/s00477-019-01677-z

Cited by 10 publications

(8 citation statements)

References 39 publications

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“…Several approaches exist for NMF for selecting the factorization rank p, but the choice of which method to use is not straightforward (Yan et al, 2019). Brunet et al (2004) suggested selecting the factorization rank based on the decrease in the cophenetic correlation coefficient (CCC), i.e.…”

Section: Determining the Number Of Factors Components Or Clustersmentioning

confidence: 99%

“…The increase is partly attributed to the new formation of the HOA component, when the HOAtype compounds in the hot exhaust gas were introduced into the chamber and contain marker ions associated with HOA (e.g. m/z 57; Zhang et al, 2005) condensed again in a cooler chamber. Meanwhile, we cannot rule out the possibility that HOA has been produced as a minor product after the photo-oxidation reaction was enabled in this study.…”

Section: Nmfmentioning

confidence: 99%

“…In addition, FN2 is characterized by the prominent peak as m/z 43. The mass spectra of FN2 and FN4 are rather similar, but FN4 has a higher contribution from m/z 44, a marker of oxygenated organic aerosol (Zhang et al, 2005), and thus it is identified as an αP-SOA-LVOOA (LVOOA -low-volatility oxygenated organic aerosol) factor. The FN3 was appointed as a mixed LVOOA.…”

Section: Nmfmentioning

confidence: 99%

“…In atmospheric studies, the latter methods have not gained widespread popularity, but a few examples still exist. Customized PCA was applied to organic aerosol data collected from Pittsburgh in 2002 (Zhang et al, 2005), and a more traditional version of PCA was used to analyse chemical-ionization-reaction time-offlight mass spectrometer (CIR-ToF-MS) and compact timeof-flight aerosol mass spectrometer (cToF-AMS) data acquired in smog chamber studies during several measurement campaigns (Wyche et al, 2015). Additionally, EFA and PCA have been applied in several source apportionment studied in the environmental science fields (Pekey et al, 2005;Sofowote et al, 2008), and a recent study on plant volatile organic compound (VOC) emissions applied EFA to separate effects of herbivory-induced stress from the natural diurnal cycle of the plants (Kari et al, 2019a).…”

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Comparison of dimension reduction techniques in the analysis of mass spectrometry data

et al. 2020

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Abstract. Online analysis with mass spectrometers produces complex data sets, consisting of mass spectra with a large number of chemical compounds (ions). Statistical dimension reduction techniques (SDRTs) are able to condense complex data sets into a more compact form while preserving the information included in the original observations. The general principle of these techniques is to investigate the underlying dependencies of the measured variables by combining variables with similar characteristics into distinct groups, called factors or components. Currently, positive matrix factorization (PMF) is the most commonly exploited SDRT across a range of atmospheric studies, in particular for source apportionment. In this study, we used five different SDRTs in analysing mass spectral data from complex gas- and particle-phase measurements during a laboratory experiment investigating the interactions of gasoline car exhaust and α-pinene. Specifically, we used four factor analysis techniques, namely principal component analysis (PCA), PMF, exploratory factor analysis (EFA) and non-negative matrix factorization (NMF), as well as one clustering technique, partitioning around medoids (PAM). All SDRTs were able to resolve four to five factors from the gas-phase measurements, including an α-pinene precursor factor, two to three oxidation product factors, and a background or car exhaust precursor factor. NMF and PMF provided an additional oxidation product factor, which was not found by other SDRTs. The results from EFA and PCA were similar after applying oblique rotations. For the particle-phase measurements, four factors were discovered with NMF: one primary factor, a mixed-LVOOA factor and two α-pinene secondary-organic-aerosol-derived (SOA-derived) factors. PMF was able to separate two factors: semi-volatile oxygenated organic aerosol (SVOOA) and low-volatility oxygenated organic aerosol (LVOOA). PAM was not able to resolve interpretable clusters due to general limitations of clustering methods, as the high degree of fragmentation taking place in the aerosol mass spectrometer (AMS) causes different compounds formed at different stages in the experiment to be detected at the same variable. However, when preliminary analysis is needed, or isomers and mixed sources are not expected, cluster analysis may be a useful tool, as the results are simpler and thus easier to interpret. In the factor analysis techniques, any single ion generally contributes to multiple factors, although EFA and PCA try to minimize this spread. Our analysis shows that different SDRTs put emphasis on different parts of the data, and with only one technique, some interesting data properties may still stay undiscovered. Thus, validation of the acquired results, either by comparing between different SDRTs or applying one technique multiple times (e.g. by resampling the data or giving different starting values for iterative algorithms), is important, as it may protect the user from dismissing unexpected results as “unphysical”.

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Section: Determining the Number Of Factors Components Or Clustersmentioning

confidence: 99%

Section: Nmfmentioning

confidence: 99%

Section: Nmfmentioning

confidence: 99%

mentioning

confidence: 99%

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Comparison of dimension reduction techniques in the analysis of mass spectrometry data

et al. 2020

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“…Several approaches exist for NMF for selecting the factorization rank p, but the choice of which method to use is not straightforward (Yan et al, 2019). Brunet et al, 2004) suggested to select the factorization rank based on the decrease in the cophenetic correlation coefficient (CCC), i.e., at the first value of p where the coefficient decreases (see, e.g., Fig.…”

Section: Determining the Number Of Factors/components/clustersmentioning

confidence: 99%

Comparison of dimension reduction techniques in the analysis of mass spectrometry data

Isokääntä¹,

Kari²,

Buchholz³

et al. 2019

Preprint

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Abstract. Online analysis with mass spectrometers produces complex data sets, consisting of mass spectra with a large number of chemical compounds (ions). Statistical dimension reduction techniques (SDRTs) are able to condense complex data sets into a more compact form while preserving the information included in the original observations. The general principle of these techniques is to investigate the underlying dependencies of the measured variables, by combining variables with similar characteristics to distinct groups, called factors or components. Currently, positive matrix factorization (PMF) is the most commonly exploited SDRT across a range of atmospheric studies, in particular for source apportionment. In this study, we used 5 different SDRTs in analysing mass spectral data from complex gas- and particle phase measurements during laboratory experiment investigating the interactions of gasoline car exhaust and α-pinene. Specifically, we used four factor analysis techniques: principal component analysis (PCA), positive matrix factorization (PMF), exploratory factor analysis (EFA), and non-negative matrix factorization (NMF), as well as one clustering technique, partitioning around medoids (PAM). All SDRTs were able to resolve 4–5 factors from the gas phase measurements, including an α-pinene precursor factor, 2–3 oxidation product factors and a background/car exhaust precursor factor. NMF and PMF provided an additional oxidation product factor, which was not found by other SDRTs. The results from EFA and PCA were similar after applying oblique rotations. For the particle phase measurements, four factors were discovered with NMF and PMF: one primary factor, a mixed LVOOA factor, and two α-pinene SOA derived factors. PAM was not able to resolve interpretable clusters due to general limitations of clustering methods, as the high degree of fragmentation taking place in the AMS causes different compounds formed at different stages in the experiment to be detected at the same variable. However, when preliminary analysis is needed, or isomers and mixed sources are not expected, cluster analysis may be a useful tool as the results are simpler and thus easier to interpret. In the factor analysis techniques, any single ion generally contributes to multiple factors, although EFA and PCA try to minimize this spread. Our analysis shows that different SDRTs put emphasis on different parts of the data, and with only one technique some interesting data properties may still stay undiscovered. Thus, validation of the acquired results either by comparing between different SDRTs or applying one technique multiple times (e.g. by resampling the data or giving different starting values for iterative algorithms) is important as it may protect the user from dismissing unexpected results as unphysical.

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Investigating the spatio-temporal variations of the impact of urbanization on haze pollution using multiple indicators

Yang

Tang

Yang

2020

Stoch Environ Res Risk Assess

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Determining the number of factors for non-negative matrix and its application in source apportionment of air pollution in Singapore

Cited by 10 publications

References 39 publications

Comparison of dimension reduction techniques in the analysis of mass spectrometry data

Comparison of dimension reduction techniques in the analysis of mass spectrometry data

Comparison of dimension reduction techniques in the analysis of mass spectrometry data

Investigating the spatio-temporal variations of the impact of urbanization on haze pollution using multiple indicators

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