Alignment and Preprocessing for Data Analysis

(1)

Alignment and Preprocessing for Data Analysis

• Preprocessing tools for chromatography

• Basics of alignment

• GC‐FID (1D) data and issues

– PCA – F‐Ratios

• GC‐MS (2D) data and issues

– PCA – F‐Ratios – PARAFAC

• Piecewise Alignment GUI (available online)

– synoveclab.chem.washington.edu/Downloads.htm – Email for username/password

(2)

Tools for Analysis: Classification

• Principal Component Analysis (PCA)

• Degree of Class Separation (DCS)

, 2 2

A B

A B

DCS D

s s

 

2 2

, ( ) ( )

A B XA XB YA YB

D    

DCS

Score PC2

Score PC1

DCS PCA Loadings`

Retention Time Retention Time

Signal Score PC2

Score PC1 Scores

X + Error

(3)

Why Align?

• Reduction in classification

– PCA

• Increase in uncertainty for quantification

– PARAFAC

• Misalignment occurs frequently

– Daily instrument variation causes misalignment – Correction is necessary to apply these methods

(4)

Retention Time Precision & PCA

DCS=32

DCS=3 PCA

PCA 10 Replicates with

limited shifting

10 Replicates with large shifting

Loadings

Retention Time

Retention Time Retention Time

Retention Time

SignalSignal __ Score PC2

Score PC1 Score PC1

Score PC2

Loadings

Scores

(5)

Basics of Alignment

• Types of alignment algorithms

– Cross correlation coefficient

– Correlation Optimized Warping (COW) – *Piecewise alignment

• Alignment Parameters

– Window Size – Shift

• Target Selection

– PCA

– Correlation Coefficient – Windowed Target

(6)

Alignment Algorithms

• Cross correlation coefficient

– Move the entire chromatogram to maximize correlation

• Correlation Optimized Warping (COW)

– Separate the chromatogram into windows

– Warp and move the windows to optimize the correlation – Find the best alignment path to correct the data

• *Piecewise alignment

– Separate the chromatogram into windows – Shift the windows to optimize the correlation – Find the best alignment path to correct the data

(7)

Alignment Parameters

Parameter

Window Size, W

Shift, L

Description Effect

Too Small Relative movement high, difficult to determine

quality of alignment

Insufficient movement of

segments

Effect Too Large

Insufficient flexibility to correct peak

to peak shifting

Increases time

Window Size ~1 pk width

0<shift<=maximum shift

Determining correct

values

Alignment Metric

L  t_R

(8)

Target Selection

• *Global Approach

– All chromatograms are initially collected – *User chosen target

– PCA optimized target

• Scores are produced for every sample

• The sample with the minimum distance from the center is the target – *Maximum correlation target

• Calculate the product of each chromatograms correlation to the others

• The maximum correlation is the target

• Online Approach

– An initial target is set

– Chromatograms are aligned as they are collected

– The target changes as new chromatograms are collected

(9)

Target Selection (Maximum Correlation)

0 2 4 6 8 10 12

0 10 20 30 40 50 60

8.05 8.1 8.15 8.2

0 1 2 3 4 5 6 7 8 9 10

0 5 10 15 20

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

0.6 Sample # 9 is the target

8.05 8.1 8.15 8.2

0 2 4 6 8 10

Type 1 Type 2 Type 3

Target Type 1 Type 2 Type 3

Retention Time, min

Signal

Retention Time, min

Signal

Sample #

Product Correlation

(10)

Alignment of GC‐FID (1D) Data and Issues

• Removal of artifacts and solvent peaks

• Baseline correction and normalization

• Alignment

• Improving PCA

– F‐Ratio

(11)

Preprocessing Tools for Chromatography

• Noise filtering

– Median filter

• Baseline correction

• Normalization

• Alignment

(12)

Experimental

• GC‐FID Separation

• 4 diesel sample types

• 9 minute separation

• 17 replicate injections over 5 days

(13)

7 7.2 7.4 7.6 7.8 0.4

0.6 0.8 1 1.2 1.4 1.6 1.8 2

Noise Filtering (Solvent, Spikes, and Outliers)

2 4 6 8 10

0 2 4 6 8 10 12 14

7 7.2 7.4 7.6 7.8

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Median Filtered Data (minimize spike)

Retention Time, min

Signal

GC-FID Separation

SignalSignal

Retention Time, min

Noise Spike

(14)

0 2 4 6 8

0 2 4 6 8 10 12

0.8 1 1.2 1.4 1.6 1.8 2 2.2

x 10⁹ -2.5

-2 -1.5 -1 -0.5 0 0.5 1 1.5x 10⁸

Outlier (low signal)

Solvent Dominated Info

Retention Time, min

Signal

GC-FID Separation

PC1

PC2

Scores Plot Solvent

(15)

0 2 4 6 8 10

0 2 4 6 8 10 12 14

1.5 2 2.5 3 3.5 4 4.5 5

x 10⁷ -3

-2 -1 0 1 2 3 4 5x 10⁶

Outlier (Low Signal)

Outlier Low Signal

Retention Time, min

Signal

GC-FID Separation

PC1

PC2

Scores Plot

(16)

0 2 4 6 8 10 0

2 4 6 8 10 12 14

No Outlier

3.4 3.6 3.8 4 4.2 4.4 4.6

x 10⁷ -3

-2 -1 0 1 2 3 4 5x 10⁶

No Outlier (Baseline / Normalization on PC1)

Retention Time, min

Signal

GC-FID Separation

PC1

PC2

Scores Plot

(17)

6.2 6.3 6.4 6.5 6.6 6.7 6.8

x 10^-3 -4

-2 0 2 4 6 8x 10^-4

0 2 4 6 8 10

-0.5 0 0.5 1 1.5 2 2.5x 10^-9

Tight Clustering in PCA

Baseline Corrected and Normalized Data

Subtract offset line from data Then divide by total signal

Retention Time, min

Normalized Signal

PC1

PC2

Scores Plot

(18)

Experimental

• GC Separation

• 3 gasoline sample types

• Misalignment is due to day to day instrument variation

(19)

Alignment GUI

Initially blank to guide the user through alignment

(20)

Load from workspace

Load from file

Alignment GUI

(21)

Zoom & Pan

Choose or Estimate Target Choose or Estimate Parameters

Load & View Data Sizes

Align Data

Alignment GUI

(22)

Now save data to workspace or .mat file

Data after alignment

Data before alignment Estimated

target and parameters

Alignment GUI

(23)

PCA Classification of Gasoline

0.038-5 0.0385 0.039 0.0395 0.04 0.0405 0.041 -4

-3 -2 -1 0 1 2 3x 10^-3

8.05 8.1 8.15 8.2 8.25 8.3 8.35

0 0.5 1 1.5 2 2.5 3

x 10^-8

We want better separation of groups

Retention Time, min

Signal

PC1

PC2

Scores Plot

(24)

Sample 1

Sample 2

Col 1

Sample 3

GC‐MS Separations

Fisher Ratio Method (F‐Ratio)

 Works well for samples that have large amounts of within class variance

 Works best when comparing a small number of sample classes

For each mass channel calculate Fisher Ratio at each point in 2D space,

Fisher Ratio =

2 2

b t w c l a s s w i t h i n c l a s s



Fisher Ratios

Col 1

(25)

0 5 10 15 0

20 40 60 80 100 120 140 160 180 200

0 5 10 15

0 100 200 300 400 500 600 700 800

Fisher Ratio Method (F‐Ratio)

8.05 8.1 8.15 8.2 8.25 8.3 8.35

0 0.5 1 1.5 2 2.5 3

x 10^-8 No alignment

After alignment

Select Top Ten

Retention Time, min

Signal

Selected Chromatographic Region

Retention Time, min

F-Ratio

Retention Time, min

F-Ratio

(26)

0 5 10 15 -1

0 1 2 3 4 5 6 7x 10^-8

Fisher Ratio Method (F‐Ratio)

5 6 7 8 9 10

x 10^-3 -1

-0.5 0 0.5 1 1.5 2 2.5x 10^-3

Retention Time, min

Signal

PC1

PC2

Scores Plot Regions of interest

Tight clustering of sample types

(27)

Summary

• Removal of solvents or artifacts is essential

• Baseline correction is an important step

• Alignment is essential for improving classification

• The F‐Ratio algorithm can further improve classification

(28)

Alignment of GC‐MS (2D) Data and Issues

• Removal of artifacts and solvent peaks

• Baseline correction and normalization

• Alignment

• Improving PCA

– F‐Ratio

• PARAFAC

(29)

Experimental

• GC‐MS Separation

(30)

Alignment GUI

Initially blank to guide the user through alignment

(31)

Load from workspace

Load from file

Alignment GUI

(32)

Zoom & Pan

Choose or Estimate Target Choose or Estimate Parameters

Load & View Data Sizes

Align Data

Alignment GUI

(33)

Now save data to workspace or .mat file

Data after alignment

Data before alignment Estimated

target and parameters

Alignment GUI

(34)

0 2 4 5

10 15 20

Alignment

TIC

Retention Time

Shift

Alignment

Total Ion Current Shift Function (TIC‐SF)

Sample Target

(35)

0 2 4 2

4 6 8 10 12

Retention Time

Shift

Total Ion Current Shift Function (TIC‐SF)

GC‐MS Data

Retention Time

Apply alignment

0 2 4

2 4 6 8 10 12

Retention Time

Sample Target

GC‐MS Data

Alignment

(36)

7.1 7.15 7.2 7.25 7.3 0

0.5 1 1.5 2 2.5

x 10^-8

7.1 7.15 7.2 7.25 7.3

0 0.5 1 1.5 2 2.5

x 10^-8

0 5 10 15

-1 0 1 2 3 4 5 6 7x 10^-8

Align

Alignment

Retention Time, min

TIC Signal TIC Signal

Retention Time, min

TIC Signal

(37)

7.05 7.1 7.15 7.2 7.25 0

0.5 1 1.5 2 2.5 3

x 10^-8

0.013-2 0.0135 0.014 0.0145 0.015

-1.5 -1 -0.5 0 0.5 1 1.5x 10^-3

PCA w/ full MS

Classification of Full MS Data

Retention Time, min

TIC Signal

PC1

PC2

Scores Plot

(38)

Sample 1 m/z Col 1

m/z Col 1

Sample 2

m/z Col 1

Sample 3

Fisher Ratios for Samples

m/z Col 1

GC‐MS Separations

Fisher Ratio Method

 Works well for samples that have large amounts of within class variance

 Works best when comparing a small number of sample classes

For each mass channel calculate Fisher Ratio at each point in 2D space,

Fisher Ratio =

2 2

b t w c l a s s w i t h i n c l a s s



Sum Fisher Ratios along mass channel dimension

Col 1

(39)

Simulated Example Using F‐Ratios for PCA

PCA

W = 400

L = 1000 _Align

Retention Time

m/z

Scores 2D F‐Ratios

Shows differences between all samples

TIC TIC

F-Ratios GC-MS Data

(40)

4.8 5 5.2 5.4 5.6 40

50 60 70 80 90 100

100 200 300 400 500 600 700

0 5 10 15

40 60 80 100 120 140

100 200 300 400 500 600 700

0 5 10 15

-1 0 1 2 3 4 5 6 7x 10^-8

F‐Ratios

Top Fisher Ratios

GC‐MS Fisher Ratios GC‐MS Fisher Ratios GC‐MS Separation

Retention Time, min

TIC Signal

(41)

Procedure

• Select masses using mass spectral information

• Select time regions using F‐Ratios

• Combine to reduce the data set

• Improve results of PCA

(42)

0 5 10 15 -1

0 1 2 3 4 5 6 7x 10^-8

Classification of Full MS Data

1.8 1.9 2 2.1 2.2 2.3 2.4

x 10^-3 -2.5

-2 -1.5 -1 -0.5 0 0.5 1 1.5x 10^-4

Clear Separation on 1^st PC

PC1

PC2

Scores Plot of Nearest Samples

Retention Time, min

Signal

Regions of interest (with MS values)

(43)

Quantification of GC‐MS Data

• Use aligned, baseline corrected and normalized data

• Use PARAFAC of small regions for analysis

– Match values to mass spectra – Peak Sums

– Peak Profiles

(44)

Quantification

• Target analyte Parallel Factor Analysis (PARAFAC) isolates the pure component peak and mass spectral information from overlapping peaks and background for both identification and quantification.

Data Matrix = Analyte 1 + Analyte 2 + ... Noise

x x

+ +…+

=

1 2

y₁ y₂

z₁ z₂

R E

Compound : malate, TMS

# of factors: 3 Chosen comp.: #3 Match value : 948 Peak sum : 4413882 Peak height : 376188

PARAFAC Results

Col. 1 Time Col. 2 Time

Intensity Intensity

(45)

1.0 1.2 1.4 1.6 0

2 4 6 8

PARAFAC for GC‐MS Data

0 2 4

2 4 6 8 10 12 14

0 2 4

2 4 6 8 10 12

Stack Samples

Retention Time

Sample

Run PARAFAC

Peak Profile

Mass Spectrum

Analyte Concentration

Sample 1

Sample 2

Sample 1

Sample 2

(46)

Experimental

• GC‐MS Separation

• Looking for isobutyl benzene in the gasoline

(47)

Isobutyl Benzene Spectrum

20 40 60 80 100 120 140 160

0 10 20 30 40 50 60 70 80 90 100

Mass

Signal

(48)

7.040 7.06 7.08 7.1 7.12 7.14 7.16 7.18 1

2 3 4 5 6x 10^-9

0 5 10 15 20 25 30 35

0 1 2 3 4 5 6 7 8 9x 10^-3

0 5 10 15 20

0 0.5 1 1.5 2 2.5 3 3.5x 10^-3

20 40 60 80 100 120 140 160

0 1 2 3 4 5 6 7x 10^-5

PARAFAC Results for GC‐MS Data

Retention Time, min

TIC Signal

Quantitative Info

Qualitative Info

Mass Spectrum

Peak Profile

Peak Sum

Selected Analysis Region for PARAFAC 1

2 3

1

2 3

1

(49)

20 40 60 80 100 120 140 160 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

20 40 60 80 100 120 140 160

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

20 40 60 80 100 120 140 160

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

MV_IBB=403 MV_IBB=788 MV_IBB=910

PARAFAC Results for GC‐MS Data

Component 1 Component 2 Component 3

Best match to isobutyl benzene

(50)

Summary

• Mass spectral chromatographic data should be aligned

• An available alignment algorithm is able to align 1‐D and 2‐D data

• F‐Ratio methods can be used to improve classification

• PARAFAC can be effectively used to separate overlapped analytes