1. 1 Status Classification of MVC Objects Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics Russian Chemometric Society Moscow

2. 2 Plan 1.Introduction 2.Main Features and Definitions of SIC- method 3.Projection Methods (PCR/PLS) and the SIC-method ( examples) 4.Conclusion

3. 3 Visualization Water with Oil X- acoustic spectra after FFT transformation (1024 variables) Y- concentration of oil in water (ppm), specially prepared samples. 40 Calibration samples 40 Test samples 40  1025

4. 4 Visualization. “2-D Projection Windows” Groups/ClustersOutliers Object spaceVariable space

5. 5 Simple interval calculation (SIC-method) Gives the result of prediction directly in an interval form Provides wide possibilities for leverage-type object status classification

6. 6 Main Assumption of SIC-method All errors are limited. Normal ( – ) distribution Finite ( – ) distributions

7. 7 The Region of Possible Values (RPV)

8. 8 SIC Prediction V-prediction interval U-test interval

9. 9 SIC main stepsRMSEC bsic

10. 10 SIC-Residual SIC-Leverage SIC Object Status Theory. Definitions

11. 11 SIC Object Status Plot

12. 12 Typical SIC- Object Status Plot Insiders Outsiders Outliers Absolute outsiders

13. 13 SIC & Projection Methods RPV Prediction Intervals Boundary Samples Insiders, Outsiders Scores Loadings Influence Plots

14. 14 PLS/PCR model Fixed number of PCs Initial Data Set {X,Y} SIC-modeling RESULTS Comparison

15. 15 Water with Oil (Data) X- acoustic spectra after FFT transformation (1024 variables) Y- concentration of oil in water (ppm), specially prepared samples. 40 Calibration samples 40 Test samples PLS-model, 2 PCs SIC-modeling bmin= 0.12 bsic=0.225 8 Boundary Samples y=log(1+y initial )

16. 16 Water with Oil. Calibration PLS (T1-U1) PLS (T2-U2) PLS Influence Plot PCs=2 SIC Object Status Plot PCs=2

17. 17 Water with Oil. Test

18. 18 Calibration set 1 {X,Y} N samples Boundary Samples and Representative Subset Selection Subset {X,Y} L samples Quality of prediction ? Calibration set 1 {X,Y} N samples Calibration set 2 {X,Y} N-L-samples

19. 19 Whole Wheat Samples X- NIR Spectra of Whole Wheat (118 wave lengths) Y- moisture content N=139 Calibration Set Data pre- processed. PLS-model, 4PCs SIC-modeling bmin= 1.03 bsic=1.53 Calibration Set- Boundary Set N-Bs(b) Boundary Subset Bs(b)

20. 20 Whole Wheat Samples

21. 21 Whole Wheat Samples Protein 6 PCs RMSEP=0.321 43 BS Gluten 6 PCs RMSEP=0.381 41 BS Moisture 4 PCs RMSEP=0.326 23 BS

22. 22

23. 23 Analysis of the Test Set Objects Norwegian Cruise Ship X- Ship/weather characteristics (7 variables) Y- Fuel consumption. 27 Calibration samples 18 Test samples PLS-model, 2PCs SIC-modeling bmin= 28.4 bsic=64.7 8 Boundary Samples

24. 24 Ship /Fuel (Calibration) PLS (T1-U1) PLS (T2-U2) SIC Object Status Plot PCs=2PLS Influence Plot PCs=2

25. 25 Ship /Fuel (Test) PLS (T1-U1)PLS (T2-U2) SIC Object Status Plot PCs=2

26. 26 Outlier detection in prediction SIC-Leverage

27. 27 DSC Example X- Oxidation Initial Temperature (OIT) at different heating rates. Y- Long Term Heating Aging (days) Total number of samples (n) =15 Number of variable (p) =5 Calibration set = 11 samples Testing set = 4 samples y-data were pre-processed. Y=Xa  Y=Tb PC’s=2 b min =0.385 b sic =0.47

28. 28 DSC Example Prediction y Object status plot

29. 29 Let D be a set in the X space defined as a linear combination of weighted calibration predictors x i Then all absolute outsiders are to be found exclusively outside this region D. The region of absolute outsiders The border of absolute outsiders

30. 30 Border of Absolute Outsider and Convex Hull DSC Example J.A. Fernandez Pierna, F.Wahl, O.E. de Noord, D.L.Massart Methods of outlier detection in prediction, ChemoLab 63 (2002) 27-39 Object status plotScore plot

31. 31 Border of Absolute Outsider and Convex Hull Norwegian Cruise Ship Object status plot. Test samples Score plot

32. 32 Test set Calibration set New objects Boundary samples Influential objects ? Absolute outsiders Outlier detection ? Object status plot Quality of test objects ?