Ulbrich PMF Tutorial - View Resultscires.colorado.edu/jimenez-group/UsrMtgs/UsersMtg9/23_Ulbrich_P… · PMF algorithm is trying to minimize this. 9 What’s the “total residual”?

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






FragmentIonTextWv


t_series => noNaNs_t_series






FragmentIonTextWv


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?


8

What’s the “total residual”?

= + … +

x

Con

tribu

tion

(µg/

m3 )

, Com

pone

nt 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


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


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


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


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


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


• Compare relative amounts of each factor

23


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


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


Residuals


34

Summary: Important Plots For Deeper Consideration

FactorsFactors


Residuals


Examination of a Real Case

Documents

Ulbrich PMF Tutorial - View Resultscires.colorado.edu/jimenez-group/UsrMtgs/UsersMtg9/23_Ulbrich_P… · PMF algorithm is trying to minimize this. 9 What’s the “total residual”?