1. St. Petersburg State University, St. Petersburg, Russia March 1st 2016
Three-point calibration models by correlation constrained MCR-ALS: A feasibility study
B. Debus, D. Kirsanov, V.V Panchuk, A.A.Goydenko, V.G Semenov, A. Legin
St. Petersburg State University, St. Petersburg, Russia
March 1st 2016

2. Background First order multivariate analysis
… and eventually get evidence of the possible interferent species
Quantitative analysis of complex mixtures in the presence of unknown interfering species
Recovery of pure individual spectral components of the target analyte

3. Validation / Prediction
Background
Partial Least Squares (PLS)
Xcal
Ycal β R2 R2
RMSEC
RMSEP
Calibration
Validation / Prediction
RE (%)
RE (%)
Strongly collinear variables / Noisy data / Prediction of more than one Y variable
For this presentation we will focus mainly on the fist part that is calibration

4. Background Calibration set design Evaluation of the number of samples
Selection of a set of uniformly distributed samples
Kennard-stone
Xcal?
k-mean X
D-optimal design
1) Large calibration set = if the number of calibration sample is too small, the predictive performance of the PLS model tends to decrease and provide biased estimates for future predictive errors.
2) Representative set of samples. 3) Kennard-stone maximum distance between pair of samples / D-optimal design = maximize the determinant of the information matrix X’X
4) k-mean and Kohonen maping = clustering techniques
5) Say that we have interest in decreasing the number of calibration samples
Xtest?
Human
decision
Reference data
Complex algorithms

5. Sample selection criterion?
Raised issues
Can we save time and efforts on calibration by using a limited number of samples?
Now the question we will try to answer today is the following. In our case we will use 3 points for the calibration.
Sample selection criterion?
Robustness / accuracy?

6. Correlation constrained MCR-ALS (CC-MCR1)k
k = bx +b0
y = bp +b0
Select profile
Update profile
C profile is divided into calibration (x) and test set prediction (p)
Build a local univariate calibration model with known concentrations (k)
Prediction of the test set concentrations based on regression coefficients (b, b0)
Everything is done in a single loop
Calibration and test set prediction are performed iteratively until convergence
All information of the dataset is used to optimize the model
1Antunes, M. C.; J. Simao, J. E.; Duarte, A. C.; Tauler, R. Analyst 2002, 127,

7. Correlation constrained MCR-ALS (CC-MCR1)
Advantages of CC-MCR
No influence on the number of samples
Possibility to recover “pure” spectral contributions
Get evidence of potential interfering species
Advantages (if we compare with standard PLS method)
Number of sample: because in PLS 3 pts = 2 LVs / for CC-MCR we work on the full C profile + (directly in concentration unit)
2) Comparison MCR components Vs PLS regression coefficients

8. Datasets Simulated datasets D1 D2 35 samples 40 samples
Uniformly distributed concentration profiles D2
40 samples

9. Datasets Real datasets 6 lanthanides mixture2 (Ce, Pr, Nd, Sm, Eu, Gd)
DTXRF
38 samples
Ternary alcohol mixture (propanol, butanol, pentanol)
Total reflection X-ray fluorescence (TXRF)
DNMR
225 samples

10. Results Simulated data D1 PLS CC-MCR Simulated profiles R2 RMSEP
Explain how the points are selected (min, max and average)
Simulated profiles R2
RMSEP
RE (%)
PLS
0.66
2.3 × 10-1
24.42
CC -MCR
0.99
6.3 × 10-3
0.73

11. Results Simulated data D2 PLS CC-MCR Simulated profiles R2 RMSEP
Do not talk about the recovery of spectra profiles because we will see it in details in the case of real samples
Simulated profiles R2
RMSEP
RE (%)
PLS
0.05
3.2 × 100
91.83
CC -MCR
0.89
4.4 × 10-1
12.43

12. Results Simulated datasets
RMSEP
RE (%)
Ncal
PLS
0.99
5.4 × 10-3
0.64
20pts
CC-MCR
5.3 × 10-3
0.62
0.66
2.3 × 10-1
24.42
3 pts
6.3 × 10-3
0.73 D2 R2
RMSEP
RE (%)
Ncal
PLS
0.98
2.0 × 10-1
6.24
30pts
CC-MCR
2.3 × 10-1
7.17
0.05
3.2 × 100
91.83
3 pts
0.89
4.4 × 10-1
12.43
Similar prediction performance when the number of calibration samples is significant
Strong increase of the prediction error for 3-pts PLS regression models
Moderate increase of the prediction error for 3-pts CC-MCR regression models

13. Results
TXRF dataset

14. Results TXRF dataset CC-MCR gives better performance than OLS and PLS
Parameters
Analyte
Method R2
RMSEP (mol/L)
RE (%) Nd
OLS
0.825
1.3 × 10-4
34.87
PLS
0.835
1.6 × 10-4
42.10
CC-MCR
0.985
4.8 × 10-5
13.02 Sm
0.645
1.7 × 10-4
54.71
0.430
3.1 × 10-4
98.99
0.982
5.8 × 10-5
14.88 % %
+ 4.5 % % %
+ 1.1 %
Say the order of magnitude is the same PLS : CC-MCR for large calibration set
Introduce the case of Sm for which PLS cannot build a predicted model (overlap)  show the slide before
CC-MCR gives better performance than OLS and PLS
Moderate increase of the relative error in predicted concentration for CC-MCR
PLS fails to build a predictive model for Sm

15. Results Reliable estimate of the signal for the target analyte
Pure spectra
Reliable estimate of the signal for the target analyte
Selectivity of the PLS model can be questioned
CC-MCR enable the estimation of possible interfering species
PLS
CC-MCR

16. Results NMR3 dataset Low S/N ratio (< 40 %)
Here we arbitrary selected Propanol and Butanol for quantitative analyse whereas Pentanol was considered as an interferent
Low S/N ratio (< 40 %)
3Winning and als. Journal of Magnetic Resonance,2008

17. Results NMR dataset Similar performance reported for PLS and CC-MCR
Parameters
Analyte
Method R2
RMSEP (%)
RE (%)
Propanol
PLS
0.993
2.362
5.72
CC-MCR
0.997
1.479
3.58
Butanol
2.343
5.60
0.998
1.248
2.98
+ 3.1 %
+ 0.5 %
+ 3.3 %
+ 0.6 %
Similar performance reported for PLS and CC-MCR
Lower error in predicted concentration for CC-MCR
Possibility to accommodate low S/N ratio with CC-MCR

18. Results Interpretation Interfering species “Pure spectra”
PLS
Interfering species
“Pure spectra”
CC-MCR
Interfering species

19. Perspectives
CC-MCR can be extended to 3-pts calibration models with reasonable relative error in predicted concentrations (4 – 15 %)
Simple selection criterion for calibration samples
Simple choice for calibration samples (min, max, average)
To a certain extend it is possible so save time, money and effort on calibration
Conclusion about NIR data (not very well appropriate)
Both qualitative and quantitative information can be derivate from CC-MCR regression models

20. Thank you for your attention
Acknowledgments
A. Legin
D. Kirsanov
VV. Panchuk
M. Khaydukova
A.A Goydenko
V.G Semenov
Thank you for your attention
Signaler que les resultats seront publies prochainement dans ACA