ulbrich pmf tutorial - view...
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1
Tutorial OutlineI. PMF Intro, Run PMF (60 min.)
• Resources for Help!• What PMF does and how it does it• Our Software Approach• Set Up our Sample Case
LUNCH (60 min.)II. Viewing Results (60 min.)
• Do the factors make physical sense?• Do the factors give a satisfactory fit to the data?
Real PMF Case (10 min.)III. Compare with External Tracers (30 min.)
• Do the factors fit with what we already know?
Preparing to View Results
1. Software knows the last PMF case you ran
2. Choose the wave that describes the COLUMNS of your data Mx
amus => noNaNs_amusExactMassWv
3. Choose the TEXT wave that describes the columns of your data Mx (or make one with the button)
FragmentIonTextWv
2
Preparing to View Results
1. Software knows the last PMF case you ran
2. Choose the wave that describes the COLUMNS of your data Mx
amus => noNaNs_amusExactMassWv
3. Choose the TEXT wave that describes the columns of your data Mx (or make one with the button)
FragmentIonTextWv
4. Choose the wave that describes the COLUMNS of your data Mx
t_series => noNaNs_t_series
Preparing to View Results
1. Software knows the last PMF case you ran
2. Choose the wave that describes the COLUMNS of your data Mx
amus => noNaNs_amusExactMassWv
3. Choose the TEXT wave that describes the columns of your data Mx (or make one with the button)
FragmentIonTextWv
4. Choose the wave that describes the COLUMNS of your data Mx
t_series => noNaNs_t_series5. Press the button!
3
PMF Evaluation Panel
What are we looking at??
4
Indicators for the Current Solution
Pop Q vs. Number of Factors 5
4
3
2
1
Q/Q
expe
cted
54321
Q for fPeak 0 Current Solution min Q for p
Q/Qexp decreases as more factors are added –more degrees of freedom in the solution.
5
Examining the Solution Factor(s)
Pop t_series14
12
10
8
6
4
2
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
• Long, straight segments in the t_series are places where there were NaNs in the original dataset
• Final plots should put the NaNs back in– See the wiki for more info!
6
The Factor Reconstructs the Data with some Residual
= + … +
x
Con
tribu
tion
(µg/
m3 )
, Com
pone
nt 1
Constant Profile,Component 1
DataMatrix
Tim
e
. . .
ResidualMatrix
. . .
Check the Reconstruction and ResidualCheck the Reconstruction and Residual
7
Pop Total Mass Reconstruction16
14
12
10
8
6
4
2
0T
otal
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
Measured Total Spec Signal Reconst Total Spec Signal
Quite good reproduction of the data with just 1 factor!
How much wasn’t fit?
Check the Reconstruction and ResidualCheck the Reconstruction and Residual
8
What’s the “total residual”?
= + … +
x
Con
tribu
tion
(µg/
m3 )
, Com
pone
nt 1
Constant Profile,Component 1
DataMatrix
Tim
e
. . .
ResidualMatrix
. . .
Σm/z
Σm/z
Σm/z
Add residual from each run
to make a residual time
series
Pop Total Residuals Tseries1.5
1.0
0.5
0.0
Σ R
esid
9/11/2002 9/13/2002 9/15/2002dat
43210Σ
Abs
(Res
id)
0.150.100.050.00
-0.05-0.10
Σ R
esid
/ΣT
otal
0.6
0.4
0.2
0.0
Σ ab
s(R
esid
)/ΣT
otal
50403020100
Σ (R
esid
2 /σ2 )
Σ resid 2/σ 2m/z
Σ |resid|m/z
Σ residm/z
Σ |resid|m/z
/org
/org
/ # m/z’s
(Q/Qexp for each run)
Σ residm/z
PMF algorithm is trying to minimize this
9
What’s the “total residual”?
= + … +
x
Con
tribu
tion
(µg/
m3 )
, Com
pone
nt 1
Constant Profile,Component 1
DataMatrix
Tim
e
. . .
ResidualMatrix
. . .
Σm/z
Σm/z
Σm/z
Add residual from each run
to make a residual time
series
OR add residual from each m/z to make a residual mass spectrum
Σruns
Σruns
Σruns
1 0 08 06 04 02 0
Check the Reconstruction and ResidualCheck the Reconstruction and Residual
10
Factor Fraction of Mass
Fraction of Mass plot
1.0
0.8
0.6
0.4
0.2
0.0
Var_Profiles Var_Tseries Var_Matrix Fract_Mass
variance_Fract_Residual variance_Fract_Factor1
Residual is ~6% of the total mass
Fraction of the Variance Fraction of the Massof each factorof the profiles
of the tseries
of the product matrix
x
11
Summary: Important Plots For First-Glance Results
FactorsFactors
Total Quality of Fit
Residuals
Factor Mass Fraction
Look at 2 factors
12
Look at 2 factors
Checking What We’re Looking at
13
Factor Profile and Time Series
• Factors are numbered from the BOTTOM up
• Colored in order of KB colorize traces
• Factors appear in an arbitrary order – Factor 1 will not always be OOA!
0.12
0.08
0.04
0.00Frac
tion
of s
igna
l
100908070605040302010m/z
0.100.080.060.040.020.00
6
4
2
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
86
4
20
1
2
1
2
Select Factor Control
14
Select Factor < 0
• All time series on same axis
• Mass spectra is total reconstructed mass spectrum, each factor profile weighted by its average mass fraction
8
6
4
2
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
80x10-3
60
40
20
0
Wei
ghte
d Fr
actio
n of
sig
nal
100908070605040302010m/z
Select Factor = 0
7
6
5
4
3
2
1
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Frac
tion
of s
igna
l
100908070605040302010m/z
8
6
4
2
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
0.10
0.08
0.06
0.04
0.02
0.00
Frac
tion
of s
igna
l
100908070605040302010m/z
1 1
2 2
Closer look at the factor selected 6
4
2
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
86
42
0
1
2
Select Factor > 0
15
Fraction of Mass
Fraction of Mass plot
1.0
0.8
0.6
0.4
0.2
0.0
Var_Profiles Var_Tseries Var_Matrix Fract_Mass
variance_Fract_Residual variance_Fract_Factor1 variance_Fract_Factor2
• 1-factor residual was 6% -- much reduced with 2 factors!
45% Factor 2
55% Factor 1
0.04% Residual
16
Check the Reconstructed MassCheck the Reconstructed Mass
Check the Reconstructed MassCheck the Reconstructed Mass
17
Stack Factors on total reconstruct16
14
12
10
8
6
4
2
0
Tot
al M
ass
9/11/2002 9/13/2002 9/15/2002dat
Measured Total Spec Signal Reconst Total Spec Signal TSeriesFactor1 TSeriesFactor2
Periods dominated by Factor 2
Periods dominated by Factor 1
Check the Reconstructed MassCheck the Reconstructed Mass
18
Total Residual time series1.5
1.0
0.5
0.0
Σ R
esid
9/11/2002 9/13/2002 9/15/2002dat
43210Σ
Abs
(Res
id)
0.150.100.050.00
-0.05-0.10
Σ R
esid
/ΣT
otal
0.6
0.4
0.2
0.0
Σ ab
s(R
esid
)/ΣT
otal
50403020100
Σ (R
esid
2 /σ2 )
0.10
0.05
0.00
-0.05
Σ R
esid
9/11/2002 9/13/2002 9/15/2002dat
0.80.60.40.20.0Σ
Abs
(Res
id)
-0.20
-0.10
0.00
0.10
Σ R
esid
/ΣTo
tal
0.6
0.4
0.2
0.0
Σ ab
s(R
esid
)/ΣT
otal
543210
Σ (R
esid
2 /σ2 )
1-Factor Solution 2-Factor Solution
Can look at 1- and 2-factor solutions together
19
Choose 1 and 2 and press the button
Can look at 1- and 2-factor solutions together
Colored in order of KB colorize traces
20
Go back to “Current”
Look at 3 factors
21
Checking what we’re looking at
Pop Q vs FPEAK0.70
0.68
0.66
0.64
Q/Q
expe
cted
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5fPeak or seed
Q for p 3 Current Solution min Q for fpeakOrSeed
FPEAK explores the bottom of the Q “well”
22
Factor Profile and Time Series
321
321
Fraction of Mass plot8
6
4
2
0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
1.0
0.8
0.6
0.4
0.2
0.0
Var_Profiles Var_Tseries Var_Matrix Fract_Mass
• Compare relative amounts of each factor
23
Check the Reconstructed MassCheck the Reconstructed Mass
Reconstructed m/z’s
24
Reconstructed mass for one m/z0.250.200.150.100.050.00
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
-20x10-3-10
01020
Res
idua
ls
Measured Spec tseries Reconst Residual SpeciesFactor1 SpeciesFactor2 SpeciesFactor3
Try a different m/z (44 and 57)
25
m/z 44 and m/z 57 species plots
1.2
0.8
0.4
0.0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
-40x10-3-20
0
2040
Res
idua
ls
-20x10-3-10
01020
Res
idua
ls
9/11/2002 9/13/2002 9/15/2002dat
0.6
0.4
0.2
0.0
Mas
s
M R R S S S
m/z 44 m/z 57
Dominated by Factor 1 Dominated by Factor 3
Species Scaled Residual distribution
80
60
40
20Freq
uenc
y of
x v
alue
-2 -1 0 1 2Scaled Residual of species 12
2
∑∑ ⎟⎟⎠
⎞⎜⎜⎝
⎛=
i j ij
ijresidQ
σ
Recall…
ij
ijresidσ
Scaled Residual for each matrix point
-2
-1
0
1
2
Scal
ed R
esid
ual
9/11/2002 9/13/2002 9/15/2002dat
-2
-1
0
1
2
Scal
ed R
esid
ual
9/11/2002 9/13/2002 9/15/2002dat
26
Species Scaled Residual distribution
1σ Gaussian scaled to max distribution height
Scaled Residuals for all m/z’s
27
Scaled Residuals for all m/z’s
6
4
2
0
-2
-4
Mas
s
1009080706050403020m/z
Boxes are +/- 25% of pointsWhiskers are +/- 5% of points
6
4
2
0
-2
-4
Mas
s
1009080706050403020m/z
Boxes are +/- 25% of pointsWhiskers are +/- 5% of points
Medians
“RR” plot
28
1.0
0.8
0.6
0.4
0.2
0.0R
, tse
ries
1.00.80.60.40.20.0R, profiles
1_2
1_3
2_3
“RR” plot
• Correlation of the factors to each otherin the same solution
See also Ulbrich et al., ACPD, 2008
321
• Labels refer to factor numbers
RMS = 1: Sources with
same MS,Retrieve
sum TSe.g., Gasoline and
Diesel vehicles
e.g., stationary sources transported
together
RTS = 1: Sources with same activity,Retrieve joint MS
Can’t resolve true factors that are near the edge
“RR” plot for “p-1” factors
29
“RR” plot for “p-1” factors1.0
0.8
0.6
0.4
0.2
0.0
R, t
serie
s
1.00.80.60.40.20.0R, profiles
1_1
1_2
2_1
2_2
3_1
3_2
• Correlation of the factors to those in the solution with 1 fewer factor
• Labels are CURRENTsolution_p-1solution
1.000
0.995
0.990
0.985
0.980
R, t
serie
s
1.0000.9950.9900.9850.980R, profiles
1_1
3_2
• Factor 3 in this 3-factor solution matches factor 2 in 2-factor solution
• Factor 1 in this 3-factor solution matches factor 1 in the 2-factor solutionCheck how much the factors change as you add more factors
Solutions with Different FPEAKs
30
Edit the Table and choose “Selected”
Solutions with Different FPEAKs
31
6420
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
86420
86420
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Fra
ctio
n of
sig
nal
504540353025201510m/z
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.10
0.08
0.06
0.04
0.02
0.00
FPEAK = -1.5FPEAK = -0.1FPEAK = +0.1FPEAK = +1.5
MS and TS change simultaneously – must consider (and report) both!
USER RESPONSIBILITY
Look at 4 factors
32
Factors and the RR plot
0.80.60.40.20.0
Mas
s
9/11/2002 9/13/2002 9/15/2002dat
6543210
86420
2.52.01.51.00.50.0
0.120.080.040.00
Frac
tion
of s
igna
l
100908070605040302010m/z
0.120.080.040.00
0.120.080.040.00
806040200
x10-3
1.0
0.8
0.6
0.4
0.2
0.0
R, t
serie
s
1.00.80.60.40.20.0R, profiles
1_2
1_3
2_3
1_4
2_4
3_4
1.0
0.8
0.6
0.4
0.2
0.0
Var_Profiles Var_Tseries Var_Matrix Fract_Mass
7%
RR plot p-1 factors
1.00
0.98
0.96
0.94
0.92
0.90
0.88
0.86
R, t
serie
s
1.000.980.960.940.92R, profiles
1_1
2_13_34_2
1.0
0.8
0.6
0.4
0.2
0.0
R, t
serie
s
1.00.80.60.40.20.0R, profiles
1_1
1_2
1_3
2_1
2_2
2_33_1
3_2
3_3
4_1
4_2
4_3
• Factors 1 and 2 in the 4-factor solution are very similar to factor 1 in the 3-factor solution
• Labels are CURRENTsolution_p-1solution
33
(almost time for)
Examination of a Real Case
(whew!)
Summary: Important Plots For First-Glance Results
FactorsFactors
Total Quality of Fit
Residuals
Factor Mass Fraction
34
Summary: Important Plots For Deeper Consideration
FactorsFactors
Total Quality of Fit
Residuals
Factor Mass Fraction
Examination of a Real Case
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