Introduction to Multivariate Calibration: A Practical Approach

✍ Scribed by Alejandro C. Olivieri

• Publisher: Springer; Second Edition 2024
• Year: 2024
• Tongue: English
• Leaves: 309
• Edition: 2
• Category: Library

✦ Synopsis

This book contains several new sections that provide even more in-depth knowledge on the topics. New content on the classical least-squares model, which shows its advantages and limitations in greater detail, was added. Additionally, the book contains a new section on the inverse least-squares model, which explains how it differs from the classical model and its applications in chemometrics. Furthermore, a new chapter on principal component analysis, which covers the concept in greater detail and its applications in chemometrics, is added. This book also includes several real-world examples to help you better understand the topic. Overall, this book provides the reader with even more comprehensive knowledge on chemometrics and multivariate calibration, making it an essential resource for students and professionals alike.

✦ Table of Contents

Foreword
Preface
About This Book
Contents
1 Chemometrics and Multivariate Calibration
1.1 Chemometrics: What’s in a Name?
1.2 The Proof is in (Eating) the Pudding
1.3 Univariate and Multivariate Calibration
1.4 Orders and Ways
1.5 Why Multivariate Calibration?
1.6 Frequently Asked Questions
1.7 Near-Infrared Spectroscopy: The Analytical Dream
1.8 Science Fiction and Chemometrics
1.9 Global Properties Versus Specific Analytes
1.10 The New Spatial Dimension
1.11 Multivariate Calibration and the Environment
1.12 Multi-way Calibration and Its New Advantages
1.13 About This Book
References
2 The Classical Least-Squares Model
2.1 Direct and Inverse Models
2.2 Calibration Phase
2.3 Model Applicability
2.4 Why Least Squares? Mathematical Requirements
2.5 Prediction Phase
2.6 The Vector of Regression Coefficients
2.7 A CLS Algorithm
2.8 Validation Phase
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
References
3 The Inverse Least-Squares Model
3.1 Why Calibrating Backwards? A Brilliant Idea
3.2 Calibration Phase
3.3 Mathematical Requirements
3.4 Prediction Phase
3.5 An ILS Algorithm
3.6 Validation Phase
3.7 Advantages and Limitations of ILS
3.8 The Successive Projections Algorithm
3.9 Other Variable Selection Algorithms for ILS
3.10 A Simulated Example
3.11 A Real Case
3.12 Another Real Case
3.13 How to Improve ILS: Ridge Regression
3.14 An RR Algorithm
3.15 How to Improve ILS: Compressed Models
3.16 Exercises
References
4 Principal Component Analysis
4.1 Why Compressing the Data?
4.2 Real and Latent Variables
4.3 The Principal Components
4.4 Highly Significant Loadings and Scores
4.5 Poorly Significant Loadings and Scores
4.6 Application to Data Exploration and Potential Sample Grouping
4.7 Class Modeling and Discrimination
4.8 The One-Class SIMCA Model
4.9 A Real Case
4.10 A PCA Algorithm
4.11 Application of PCA to Multivariate Calibration
4.12 Exercises
References
5 Principal Component Regression
5.1 PCA and ILS Combined: Another Brilliant Idea
5.2 Matrix Compression and Decompression
5.3 Calibration Phase
5.4 Mathematical Requirements
5.5 Prediction and Validation Phases
5.6 The Vector of Regression Coefficients
5.7 Karl Norris and the Regression Coefficients
5.8 A PCR Algorithm
5.9 How Many Latent Variables?
5.10 Advantages of PCR
5.11 A Real Case
5.12 What Can Be Better Than PCR?
5.13 Exercises
References
6 The Optimum Number of Latent Variables
6.1 How Many Latent Variables?
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 A Real Case
6.10 Exercises
References
7 The Partial Least-Squares Model
7.1 The PLS Philosophy
7.2 Calibration Phase
7.3 Mathematical Requirements and Latent Variables
7.4 Prediction and Validation Phases
7.5 The Vector of Regression Coefficients
7.6 A PLS Algorithm
7.7 The First-Order Advantage
7.8 Real Cases
7.9 PLS-1 and PLS-2
7.10 A PLS-2 Algorithm
7.11 PLS—Discriminant Analysis
7.12 Another Real Case
7.13 Advantages of PLS
7.14 Beyond PLS
7.15 Exercises
References
8 Models Considering the Noise Structure
8.1 Noise Structures
8.2 The Error Covariance Matrix
8.3 Maximum Likelihood PCR
8.4 An MLPCR Algorithm
8.5 Error Covariance Penalized Regression
8.6 An EPCR Algorithm
8.7 A Real Case
8.8 Another Real Case
8.9 Exercises
References
9 Sample and Sensor Selection
9.1 Pre-calibration Activities
9.2 Sample Selection
9.3 An Algorithm for Kennard–Stone Sample Selection
9.4 Calibration Outliers
9.5 Sensor Selection
9.6 Regression Coefficients for Selecting Sensors
9.7 Interval-PCR/PLS
9.8 A Real Case
9.9 Other Sensor Selection Methods
9.10 Exercises
References
10 Mathematical Pre-processing
10.1 Why Mathematical Pre-processing
10.2 Mean Centering
10.3 Smoothing and Derivatives: Benefits and Hazards
10.4 An Algorithm for Smoothing and Derivatives
10.5 Multiplicative Scattering Correction
10.6 Additional Pre-processing Methods
10.7 Algorithms for MSC, SNV and DETREND
10.8 How to Choose the Best Mathematical Pre-processing
10.9 Is Pre-processing Always Useful?
10.10 A Simulated Example
10.11 A Real Case
10.12 Calibration Update
10.13 A PDS Algorithm
10.14 Exercises
References
11 Analytical Figures of Merit
11.1 Figures of Merit: What for?
11.2 Sensitivity
11.3 Selectivity
11.4 Prediction Uncertainty
11.5 The Effect of Mathematical Pre-processing
11.6 The Effect of the Noise Structure
11.7 Detection Limit
11.8 The Blank Leverage
11.9 Quantitation Limit
11.10 Other Figures of Merit
11.11 Real Cases
11.12 A Real Case of Non-iid Noise
11.13 Exercises
References
12 MVC1: Software for Multivariate Calibration
12.1 Downloading and Installing the Software
12.2 General Characteristics
12.3 Real Cases Studied with MVC1
12.4 Bromhexine in Cough Syrups
12.5 Prediction Outliers in the Bromhexine Example
12.6 A Dinitro-Cresol in Reaction Mixtures
12.7 Moisture, Oil, Protein, and Starch in Corn Seeds
12.8 Protein in Wheat
12.9 Additional MVC1 Models
12.10 Other Programs
12.11 Exercises
References
13 Non-linearity and Artificial Neural Networks. Radial Basis Functions and Kernel Partial Least-Squares
13.1 Linear and Non-linear Problems
13.2 Multivariate Non-linearity Tests
13.3 A Durbin-Watson Algorithm
13.4 Non-linear Relationships and Projections
13.5 Artificial Neural Networks
13.6 Radial Basis Functions
13.7 An RBF Algorithm
13.8 RBF Networks in MVC1
13.9 A Real Case
13.10 Figures of Merit
13.11 Kernel Partial Least-Squares
13.12 KPLS in MVC1
13.13 Exercises
References
14 Non-linearity and Artificial Neural Networks. Multi-layer Perceptron
14.1 Multi-layer Perceptron Networks
14.2 Learning by Backpropagation of Errors
14.3 Figures of Merit
14.4 MLP in MVC1
14.5 Some Final Reflections on Neural Networks
14.6 Exercises
References
15 Solutions to Exercises
15.1 Chapter 2
15.2 Chapter 3
15.3 Chapter 4
15.4 Chapter 5
15.5 Chapter 6
15.6 Chapter 7
15.7 Chapter 8
15.8 Chapter 9
15.9 Chapter 10
15.10 Chapter 11
15.11 Chapter 12
15.12 Chapter 13
15.13 Chapter 14
Reference