department of science u.s. coast guard academy new london, connecticut [email protected]

Department of ScienceU.S. Coast Guard AcademyNew London, [email protected]

LCDR Gregory J. HallGlenn S. Frysinger

Chemometric Methods for GC x GC

LCDR Gregory J. Hall1995 B.S. Marine Science – U.S. Coast Guard

Academy

1995 – 1997 Operations Officer, USCGC SPAR

1997-1998 M.S. Chemistry, Tufts University

1998-2000 Rotating Military Faculty, USCGA

2000 – Appointed to the PCTS

2002 – 2004 Ph.D. sabbatical, Tufts University

2006 – Ph.D. Chemistry, Tufts University“Chemometric Characterization and Classification of Estuarine Water through Multidimensional Fluorescence”

Permanent Commissioned Teaching Staff (PCTS)

About 23 officers ranked from LT to CAPT

Provide the “interpreters” between the military and civilian faculty and leadership for the college

Teaching, Service, and Scholarship expected

Ph.D. required

LCDR Gregory J. Hall

What IS Chemometrics?Chemometrics is the chemical discipline that uses mathematical, statistical and other methods employing formal logic to design or select optimal measurement procedures and experiments, and to provide maximum relevant chemical information by analyzing chemical data. (D.L. Massart: Chemometrics:, Elsevier, NY,1988)

Chemometrics already covered and to come

1. Difference Chromatograms

2. Property Modeling

3. Clustering

4. Chromatograph Prediction

5. Mass Spec searching

6. Template Construction

7. XICs

8. Retention Indices

You are all already chemometricians!

Today1. Data Structures – How I view GC x GC data

2. Variance - PCA

3. Classification – SIMCA, PCR-DA

4. Regression – PLS

5. Peak Resolution - PARAFAC

6. Preprocessing – Alignment

7. The way forward, humble opinions

Data – GC x GC - FID

XJ

K

I

sam

ple

First Dimension

Secon

d Dim

ensio

n

1 2 40 50 67 32 32 25 10 1

2 5 64 90 45 1 18 5 67 10 1

7 41 7 80 23 4 41 50 42 20

Intensity Values

Chromatogram

“Two way”

3 Dimensions

Chromatogram Stack

“Three way”

4 Dimensions

Dataset Data Object

First DimensionSec

ond

Dimen

sion

Data – GC x GC -TOF

Sample (Date?)

First Dimension

Secon

d Dim

ensio

n

m/z

X

Dataset

“Four way”

5 Dimensions !

variable 1

varia

ble

2va

riabl

e 3

ij

PC 1

PC 2

T2Q

Principal Components Analysis (PCA)

Principal Components Analysis (PCA)

= T

P

“model”

Sam

ples

X

data

E+

residuals

“components”

X T P E

Goal - Variance capture

Multi-way Principal Components Analysis (MPCA)

Wise, B. M.; Gallagher, N. B.; Bro, R.; Shaver, J. M.; Windig, W.; Koch, R. S. PLS Toolbox 4.0; Eigenvector Research, Inc.: Wenatchee, WA, 2006.

Our data15 x 410,000

0 5 10 15 20 25 30 35 40

3.0

2.0

1.0

0.0

Time (min)

Tim

e (s

)

4.0

GC × GC/MS TIC of Fire Debris

6 clean carpet samples 5 gasoline samples6 “doped” carpet samples

PCA Model Specifics1. Only two carpet classes included

2. 4 PCs = 98% variance

3. Two random samples per class left out, all gasoline samples left out of “training set”

4. Left out samples “projected” onto the model later.

PC 1 - LoadingsPC 1 - Loadings

0 5 10 15 20 25 30 35 40 45 50

2.0

1.5

1.0

0.5

0

Time (min)

Tim

e (s

)

Red = positive loadings, correlatedBlue = negative loadings, anti-correlated

PC 2 - LoadingPC 2 - Loading

0 5 10 15 20 25 30 35 40 45 50

2.0

1.5

1.0

0.5

0

Time (min)

Tim

e (s

)

Chemically interpretable results!Next step - classification

Principal Components RegressionDiscriminant Analysis (PCR-DA) w/

accelerant

wo/ accelerant

0 1

0 1

0 1

0 1

1 0

1 0

1 0

1 0

1 0

Y

0 5 10 15 20 25 30 35 40 45 50

2.0

1.5

1.0

0.5

0Time (min)

Tim

e (s

)0 5 10 15 20 25 30 35 40 45 50

2.0

1.5

1.0

0.5

0Time (min)

Tim

e (s

)0 5 10 15 20 25 30 35 40 45 50

2.0

1.5

1.0

0.5

0Time (min)

Tim

e (s

)

Xvariable 1

varia

ble

2va

riabl

e 3

ij

PC 1

PC 2

T2Q

Regression Vector

Regression VectorRegression Vector

0 5 10 15 20 25 30 35 40 45 50

2.0

1.5

1.0

0.5

0

Time (min)

Tim

e (s

)

Red = positive loadingsBlue = negative loadings

20 25 30

150

100

O

Regression Vector ZoomRegression Vector Zoom

Principal Components Regression Principal Components Regression PredictionsPredictions

1 6 7 12 17-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Sample Scores on the Regression Vector

Unaltered Carpet

Arson Debris

Gasoline

Discriminant Analysis 1 = Member of Arson Class

Classification – Soft Independent Model of Class Analogy (SIMCA)

variable 1

varia

ble

2va

riabl

e 3

xy

zk

22 2xk r rd Q T

22

, , 20.95 0.95

k kr k r k

Q TQ TQ T

variable 1va

riable

2

varia

ble

3

ij

PC 1

PC 2

T2Q

SIMCA Model Specifics1. PCA modeled for 2 classes – Arson , not Arson

2. Each model had 2 PCs with 99% variance captured

3. One random samples per class left out, all gasoline samples left out of “training set”

4. Left out samples “projected” onto each model later.

Arson “Case” SIMCA Results

Carpet Doped Gasoline0

1

In C

arpe

t Cla

ss

0

1

In D

oped

Cla

ss

1

2

Nea

rest

Cla

ss

0

1N

ot in

any

Cla

ss

Carpet Doped Gasoline

Carpet Doped GasolineCarpet Doped Gasoline

Carpet SamplesCarpet TestDoped SamplesDoped TestGasoline Test

Arson “Case” SIMCA Fit Statistics

-10 0 10 20 30-0.01

0

0.01

0.02

0.03

0.04

Q Residuals

T^2

Res

idua

ls

0 50 100 150 200 250

0

0.05

0.1

0.15

0.2

0.25

Q ResidualsT^

2 R

esid

uals

Fit Statistics for Doped Carpet Class

-4 -2 0 2 4 6 80.01

0.015

0.02

0.025

0.03

Q Residuals

T^2

Res

idua

ls

0 500 1000

0

0.2

0.4

0.6

0.8

1

Q Residuals

T^2

Res

idua

ls

Fit Statistics for Carpet Class

Carpet SamplesCarpet TestDoped SamplesDoped TestGasoline Test

Parallel Factor Analysis (PARAFAC)

1

R

ijk ir jr kr ijkr

x a b c e

+=

B

A

CG

X E

+=X E

a1

b1

c1

a2

b2

c2

a3

b3

c3

+ +

J

K

I

J

K

I

J

R

K R

R I

J

K

I

J

K

I


PARAFAC

Sample

Sco

reLo

adin

g

Load

ing

First Dimension Second DimensionXJ

K

I

Factor 1Factor 2

a1

b1

c1

a2

b2

c2

Sample

Sco

reLo

adin

g

Load

ing

First Dimension

GC x GC - FID

Chromatogram Stack

Second Dimension


GC x GC - TOF

Sinha, A. E.; Fraga, C. G.; Prazen, B. J.; Synovec, R. E. Journal of Chromatography A 2004, 1027, 269-277.


PARAFAC

m/z

Sco

reLo

adin

g

Load

ing

First Dimension Second DimensionXJ

K

I

Factor 1Factor 2

a1

b1

c1

a2

b2

c2

m/z

Sco

reLo

adin

g

Load

ing

First Dimension

GC x GC - TOF

Sample

Second Dimension


GC x GC - TOF

“Complex Environmental Sample”


PARAFAC Results


GCImage screen capture

NIJ0221 100 µg 75% Wx gasoline / nylon carpet matrix

GC × GC/MS Peak Deconvolution PARAFAC?

Partial Least Squares (PLS)

X T P E Y T Q F

= T

P

“model”

sam

ples

X

data

E+

residuals

“latent variables”

Y

variables

sam

ples

properties

= TFQ +

PLS Results Naphthalenes in Jet Fuel

Johnson, K. J.; Prazen, B. J.; Young, D. C.; Synovec, R. E. Journal of Separation Science 2004, 27, 410-416.

Alignment Strategy 1Experimental Design

Alignment Strategy 2Templates / Peak TablesAlignment Strategy 3Retention Index

Alignment Strategy 4Piecewise Correlation Maximization

Pierce, K. M.; Wood, L. F.; Wright, B. W.; Synovec, R. E. Analytical Chemistry 2005, 77, 7735-7743.

Alignment Strategy 5

“Warping”

Kaczmarek, K.; Walczak, B.; de Jong, S.; Vandeginste, B. G. M. Journal of Chemical Information and Computer Sciences 2003, 43, 978-986.

Alignment Strategy Proposal # 1Anchor Warping

Alignment Strategy Proposal #2DTW – Piecewise Hybrid

1st Dimension DTW Alkanes?

2nd Dimension Piecewise

Humble Opinions1. GC x GC is tremendously interesting data

2. Tremendous amounts of work possible, even with data that presently exists. Good alignment will open up even more possibilities

3. Include the Chemist in the analysis

4. Include the Chemometrician in the experimental design

Future? 1. More PCA, PCR, PLS, PARAFAC

2. Regression certainty calculations

3. NPLS, NPLS-DA

4. Holistic, automatic alignment strategies 2D COW or DTW ?

PARAFAC 2 ?

5. User driven alignment strategiesAnchor warping

6. Inclusion on m/z axisPurity, CODA?

U.S. Coast Guard Academy Alexander Trust

You all!

Acknowledgements

department of science u.s. coast guard academy new london, connecticut [email protected]

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