1. Chemometric functions in Excel
Oxana Rodionova & Alexey Pomerantsev
Semenov Institute of Chemical Physics

2. Distance Learning Course in Chemometrics for Technological and Natural-Science Mastership Education
Unfulfilled need in chemometric education in Russia
Low number of qualified specialists in chemometrics
Large distances, e.g. Moscow – Barnaul is about 3000 km
No modern chemometrics books in Russian
No available chemometric software
No support from officials: government, Academy, etc
3000 km
Easy available everywhere => INTERNET
Interactive layout: all calculations should be clear and repeatable
Web friendly environment for the calculations => EXCEL
Necessity to make and use our own (free) software => EXCEL Add-In
4000 km
Barnaul

3. Chemometric calculations in Excel
Provides user with all possibilities of Excel interface, worksheet calculations, worksheet functions, charts, etc.
VBA helps to simplify routine work
All calculations are made "on the fly“ and very fast

4. Installation http://rcs.chph.ras.ru/down/sacs.zip
Chemometrics.dll  put in your Windows folder
(C:\WINDOWS\)
Chemometrics. xla 
put in the AddInn folder
(C:\Documents and Settings\ <User>\Application Data\ Microsoft\AddIns\)
Load Chemometrics.xla by < Excel Options>  <Add-Ins> in the open Workbook

5. Matrix calculations in Excel
={TRANSPOSE(B6:F10)}
Ctrl-Shift-Enter
B6:F10
Barr
={MMULT(B6:F10,TRANSPOSE(Barr))}

6. Principal Component Analysis (PCA)
Initial data = + ×
Error matrix E I J A
Score matrix T I
Loading matrix X P J A PT J A I J
X=TPT+E

7. Chemometrics XLA. PCA Scores
Xcal
Xtst
Centering AND/OR weighting
={ScoresPCA(Xcal,5,1,Xtst)}
nPC

8. Chemometrics XLA. PCA Loadings
Xcal
Excel worksheet function
=TRANSPOSE(LoadingsPCA(Xcal,5,1))}
nPC
Centering AND/OR weighting

9. List of chemometric functions
PCA
ScoresPCA <for calibration or test samples>
LoadingsPCA
PLS
ScoresPLS <X-scores for calibration or test samples>
UScoresPLS <Y-scores for calibration or test samples>
LoadingsPLS <P-loadings>
WLoadingsPLS
QLoadingsPLS
PLS2
ScoresPLS2 <X-scores for calibration or test samples>
UScoresPLS2 <Y-scores for calibration or test samples>
LoadingsPLS2 <P-loadings>
WLoadingsPLS2
QLoadingsPLS2
Options:
Centering AND/OR scaling
Number of PCs

10. X data (calibration set)
ScoresPCA
X data (calibration set)
ScoresPCA (rMatrix [, nPCs] [,nCentWeightX] [, rMatrixNew] ) 
Number of PC (A)
Test set
centering and/or scaling
1 centering
2 scaling
3 both
X[IJ]  T[I A]

11. 10% -out cross-validation
Validation Rules
If rMatrixNew is omitted then only calibration scores are calculated
If rMatrixNew is specified then only test scores are calculated
If rMatrixNew coincides with rMatrix then cross-validation is calculated
10% -out cross-validation

12. X data (calibration set)
LoadingsPCA
X data (calibration set)
LoadingsPCA (rMatrix [, nPCs] [,nCentWeightX]) 
Number of PC (A)
centering and/or scaling
1 centering
2 scaling
3 both
X[IJ]  P[J A]

13. Explorative Data Analysis
Case study 1: People

14. People

15. Dataset in Excel Workbook (People.xls)
Number of objects (n) = 32
Number of variables (m) = 12

16. Data Preprocessing
Aim: to transform the data into the most suitable form for data analysis

17. Autoscaling
mean centering
scaling
autoscaling + =

18. People: Scores & Loadings (PC1 vs. PC2)
“Map of Samples”
“Map of Variables”

19. People: Scores & Loadings (PC1 vs. PC3)
Loading plot
Score plot

20. Case study 2: HPLC-DAD

21. Measurements

22. Dataset in Excel Workbook

23. If we observe X can we predict C and S ?
Pure compounds A and B
If we observe X can we predict C and S ?
X=CST+E

24. Score plot A B

25. Conclusions from the Score Plot
1. Linear regions = Pure compounds 2. Curved line= Co-elution 3. Closer to the origin = Lower intensity 4. Number of bends = Number of different compounds

26. Factor analysis vs. PCA analysisX E1 + = C ST × 2 J I X E2 + = T PT × A J I

27. Scores and Loadings

28. Procrustes transformation
X ≈ CST
X ≈ TPT
I = RRT = Identity matrix
X ≈ T(RRT)PT = (TR)(PR)T
C ≈ TR S ≈ PR
R = Rstretch ×Rrotation ^ ^

29. Scores Transformation
Stretching
Rotation

30. Procrustes analysis results

31. Conclusions Scaling and centering is problem dependent
In this example number of PCs = Number of different compounds

32. Regression

33. Principal Component Regression (PCR)1 t A
... P T X
1) PCA y T a = + e 
2) MLR

34. Projection on Latent Structures (PLS)Q U P T W p 1 t A
... X u 1 A
... q t Y w 1 t A
...

35. Projection on Latent Structures (PLS)B = + e  Y

36. PLS and PLS2 b = + e  y T 1
PLS B = + E  Y T M
PLS2

37. ScoresPLS X[IJ], Y[I1]  T[IA]
X data (calibration set)
Y data (calibration set)
ScoresPLS (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew])
Number of PC (A)
X Test set
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[I1]  T[IA]

38. UScoresPLS X[IJ] , Y[I1]  U[I A]
X data (calibration set)
Y data (calibration set)
UScoresPLS (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew] [, rMatrixYNew])
Number of PC (A)
X Test set
Y Test set
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ] , Y[I1]  U[I A]

39. WLoadingsPLS X[IJ] , Y[I1]  W[J A]
X data (calibration set)
Y data (calibration set)
WLoadingsPLS (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY])
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ] , Y[I1]  W[J A]

40. LoadingsPLS X[IJ] , Y[I1]  P[JA]
X data (calibration set)
Y data (calibration set)
LoadingsPLS (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY])
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ] , Y[I1]  P[JA]

41. QLoadingsPLS X[IJ], Y[I1]  Q[1 A]
X data (calibration set)
Y data (calibration set)
QLoadingsPLS (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY])
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[I1]  Q[1 A]

42. ScoresPLS2 X[IJ], Y[IK]  T[I A]
X data (calibration set)
Y data (calibration set)
ScoresPLS2 (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew])
Number of PC (A)
X Test set
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[IK]  T[I A]

43. UScoresPLS2 X[IJ], Y[IK]  U[I A]
X data (calibration set)
Y data (calibration set)
UScoresPLS2 (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew] [, rMatrixYNew])
Number of PC (A)
X Test set
Y Test set
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[IK]  U[I A]

44. LoadingsPLS2 WLoadingsPLS2 QLoadingsPLS2
X data (calibration set)
Y data (calibration set)
LoadingsPLS2 (rMatrixX, rMatrixY [, nPCs] [, nCentWeightX] [, nCentWeightY])
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[IK]  P[J A] or W[J A] or Q[K A]

45. Seventh Winter Symposium on Chemometrics
near Tula city, February 2010
100 km