Introduction to Multivariate Calibration: A Practical Approach - Softcover

Olivieri, Alejandro C.

Softcover

ISBN 10: 3319970984 ISBN 13: 9783319970981

Publisher: Springer, 2018

Synopsis

1. Chemometrics and multivariate calibration

1.1. Chemometrics: what's in a name?

1.2. Univariate and multivariate calibration

1.3. The order and the ways

1.4. Why multivariate calibration?

1.5. Near infrared spectroscopy: the analytical dream

1.6. Multi-way calibration and new advantages

1.7. References

 

2. First-order multivariate models: CLS

2.1. Direct and inverse models

2.2. Classical least-squares

2.3. The CLS calibration phase

2.4. Why least-squares? Mathematical requirements

2.5. The CLS prediction phase

2.6. The CLS vector of regression coefficients

2.7. A CLS algorithm

2.8. Validation of the CLS model

2.9. Spectral residuals and sample diagnostic

2.10. The first-order advantage

2.11. A real case

2.12. Advantages and limitations of CLS

2.13. Exercises

2.13. References

 

3. First-order multivariate models: ILS

3.1. Why calibrating the other way around? A fantastic idea

3.2. The ILS calibration phase

3.3. Mathematical requirements

3.4. The ILS prediction phase

3.5. An ILS algorithm

3.6. The validation of the ILS model

3.7. Advantages and limitations of ILS

3.8. The successive projections algorithm

3.9. A real case

3.10. How to improve ILS

3.11. Exercises

3.12. References

 

4. Principal component analysis: PCA

4.1. Why compressing the data?

4.2. Real and latent variables

4.3. Principal components

4.4. Significant loadings and scores

4.5. Non-significant loadings and scores

4.6. Sample classification with PCA

4.7. Multivariate calibration with PCA

4.8. Exercises

4.9. References

 

5. First-order multivariate models: PCR

5.1. Combination of PCA and ILS: another fantastic idea

5.2. Matrix compression and decompression

5.3. The PCR calibration phase

5.4. Mathematical requirements

5.5. The PCR prediction phase

5.6. The PCR vector of regression coefficients

5.7. A PCR algorithm

5.8. What is the value of A?

5.9. Advantages and limitations of PCR

5.10. A real case

5.11. What can be better than PCR?

5.12. Exercises

5.13. References

 

6. The optimum number of latent variables

6.1. The importance of estimating the optimum A

6.2. Explained variance

6.3. Visual inspection of loadings

6.4. Leave-one-out cross validation

6.5. Cross-validation statistics

6.6. Monte Carlo cross-validation

6.7. Other methods

6.8. The principle of parsimony

6.9. Beyond statistics: physicochemical interpretation of A

6.10. Exercises

6.11. References

 

7. First-order multivariate models: PLS

7.1. The PLS philosophy

7.2. The PLS calibration phase

7.3. Mathematical requirements

7.4. The number of latent variables

7.5. The PLS prediction phase

7.6. The vector of PLS regression coefficients

7.7. A PLS algorithm

7.8. Advantages and limitations of PLS

7.9. A real case

7.10. PLS-1 and PLS-2 models

7.11. Discriminant PLS

7.12. Beyond PLS

7.12. Exercises

7.13. References

 

8. Comparison of models

8.1. Which is the best model?

8.2. The randomization test

8.3. How the test works

8.4. Algorithm for the randomization test

8.5. PCR, PLS-1 and PLS-2: when, how and why

8.6. Linear and non-linear models: when, how and why

8.7. Tests of multivariate non-linearity

8.8. A real case

8.9. Conclusions

8.10. References

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Edition details

• Publisher: Springer
• Publication date: 2018
• Language: English
• ISBN 10: 3319970984
• ISBN 13: 9783319970981
• Binding: Paperback
• Number of pages: 264