Chemometrics and Numerical Methods in LIBS A practical guide to the application of chemometric methods to solve qualitative and quantitative problems in LIBS analyses Chemometrics and Numerical Methods in LIBS, delivers an authoritative and practical exploration of the use of advanced chemometric methods to laser-induced breakdown spectroscopy (LIBS) cases. The book discusses the fundamentals of chemometrics before moving on to solutions that can be applied to data analysis methods. It is a concise guide designed to help readers at all levels of knowledge solve commonly encountered problems in the field. The book includes three sections: LIBS information simplification, LIBS classification, and quantitative analysis by LIBS. Each section of the book is divided into a description of relevant techniques and practical examples of its applications. Contributors to this edited volume are the most recognized international experts on the chemometric techniques relevant to LIBS analysis. Chemometrics and Numerical Methods in LIBS also includes: A thorough introduction to the simplification of LIBS information, including principal component analysis, independent component analysis, and parallel factor analysis Comprehensive explorations of classification by LIBS, including spectral angle mapping, linear discriminant analysis, graph clustering, self-organizing maps, and artifical neural networks Practical discussions of linear methods for quantitative analysis by LIBS, including calibration curves, partial least squares regression, and limit of detection In-depth examinations of multivariate analysis and non-linear methods, including calibration-free LIBS, the non-linear Kalman filter, artificial and convolutional neural networks for quantification Relevant for researchers and PhD students seeking practical information on the application of advanced statistical methods to the analysis of LIBS spectra, Chemometrics and Numerical Methods in LIBS will also earn a place in the libraries of students taking courses involving LIBS spectro-analytical techniques

Table of Contents:
List of Contributors xiii Preface xvii Introduction and Brief Summary of the LIBS Development 1 Part I Introduction to LIBS 5 1 LIBS Fundamentals 7 Mohamad Sabsabi 1.1 Interaction of Laser Beam with Matter 8 1.2 Basics of Laser–Matter Interaction 9 1.3 Processes in Laser-Produced Plasma 10 1.4 Factors Affecting Laser Ablation and Laser-Induced Plasma Formation 11 1.4.1 Influence of Laser Parameters on the Laser-Induced Plasmas 11 1.4.2 Laser Wavelength (λ) 12 1.4.3 Laser Pulse Duration (τ) 12 1.4.4 Laser Energy (E) 13 1.4.5 Influence of Ambient Gas 13 1.5 Plasma Properties and Plasma Emission Spectra 14 References 15 2 LIBS Instrumentations 19 Mohamad Sabsabi and Vincenzo Palleschi 2.1 Basics of LIBS instrumentations 19 2.2 Lasers in LIBS Systems 20 2.3 Desirable Requirements for Atomic Emission Spectrometers/Detectors 22 2.4 Spectrometers 23 2.4.1 Czerny–Turner Optical Configuration 23 2.4.2 Paschen–Runge Design 24 2.4.3 Echelle Spectrometer Configuration 25 2.5 Detectors 26 2.5.1 Photomultiplier Detectors 26 2.5.2 Solid-State Detectors 27 2.5.3 The Interline CCD Detectors 27 2.5.3.1 The Image Intensifier 28 References 29 3 Applications of LIBS 31 Vincenzo Palleschi and Mohamad Sabsabi 3.1 Industrial Applications 31 3.1.1 Metal Industry 31 3.1.2 Energy Production 34 3.2 Biomedical Applications 34 3.3 Geological and Environmental Applications 36 3.4 Cultural Heritage and Archaeology Applications 37 3.5 Other Applications 37 References 38 Part II Simplications of LIBS Information 45 4 LIBS Spectral Treatment 47 Sabrina Messaoud Aberkane, Noureddine Melikechi and Kenza Yahiaoui 4.1 Introduction 47 4.2 Baseline Correction 47 4.2.1 Polynomial Algorithm 48 4.2.2 Model-free Algorithm 49 4.2.3 Wavelet Transform Model 52 4.3 Noise Filtering 55 4.3.1 Wavelet Threshold De-noising (WTD) 55 4.3.2 Baseline Correction and Noise Filtering 59 4.4 Overlapping Peak Resolution 60 4.4.1 Curve Fitting Method 61 4.4.2 The Wavelet Transform 64 4.5 Features Selection 66 4.5.1 Principal Component Analysis 68 4.5.2 Genetic Algorithm (GA) 68 4.5.3 Wavelet Transformation (WT) 68 References 71 5 Principal Component Analysis 81 Mohamed Abdel-Harith and Zienab Abdel-Salam 5.1 Introduction 81 5.1.1 Laser-Induced Breakdown Spectroscopy (LIBS) 81 5.2 The Principal Component Analysis (PCA) 82 5.3 PCA in Some LIBS Applications 83 5.3.1 Geochemical Applications 83 5.3.2 Food and Feed Applications 85 5.3.3 Microbiological Applications 88 5.3.4 Forensic Applications 91 5.4 Conclusion 94 References 94 6 Time-Dependent Spectral Analysis 97 Fausto Bredice, Ivan Urbina, and Vincenzo Palleschi 6.1 Introduction 97 6.2 Time-Dependent LIBS Spectral Analysis 98 6.2.1 Independent Component Analysis 98 6.2.2 3D Boltzmann Plot 102 6.2.2.1 Principles of the Method 103 6.3 Applications 109 6.3.1 3D Boltzmann Plot Coupled with Independent Component Analysis 109 6.3.2 Analysis of a Carbon Plasma by 3D Boltzmann Plot Method 109 6.3.3 Assessment of the LTE Condition Through the 3D Boltzmann Plot Method 114 6.3.4 Evaluation of Self-Absorption 114 6.3.5 Determination of Transition Probabilities 118 6.3.6 3D Boltzmann Plot and Calibration-free Laser-induced Breakdown Spectroscopy 121 6.4 Conclusion 123 References 123 Part III Classification by LIBS 127 7 Distance-based Method 129 Hua Li and Tianlong Zhang 7.1 Cluster Analysis 132 7.1.1 Introduction 132 7.1.2 Theory 133 7.1.2.1 K-means Clustering 133 7.1.2.2 Hierarchical Clustering 134 7.1.3 Application 135 7.2 Independent Components Analysis 138 7.2.1 Introduction 138 7.2.2 Theory 138 7.2.3 Application 140 7.3 K-Nearest Neighbor 143 7.3.1 Introduction 143 7.3.2 Theory 143 7.3.3 Application 145 7.4 Linear Discriminant Analysis 145 7.4.1 Introduction 145 7.4.2 Theory 148 7.4.2.1 The Calculation Process of LDA (Two Categories) 148 7.4.3 Application 151 7.5 Partial Least Squares Discriminant Analysis 153 7.5.1 Introduction 153 7.5.2 Theory 155 7.5.3 Application 157 7.6 Principal Component Analysis 161 7.6.1 Introduction 161 7.6.2 Theory 164 7.6.3 Application 166 7.7 Soft Independent Modeling of Class Analogy 174 7.7.1 Introduction 174 7.7.2 Theory 175 7.7.3 Application 177 7.8 Conclusion and Expectation 180 References 181 8 Blind Source Separation in LIBS 189 Anna Tonazzini, Emanuele Salerno, and Stefano Pagnotta 8.1 Introduction 189 8.2 Data Model 193 8.3 Analyzing LIBS Data via Blind Source Separation 193 8.3.1 Second-order BSS 193 8.3.2 Maximum Noise Fraction 194 8.3.3 Independent Component Analysis 196 8.3.4 ICA for Noisy Data 197 8.4 Numerical Examples 197 8.5 Final Remarks 206 References 207 9 Artificial Neural Networks for Classification 213 Jakub Vrábel, Erik Képeš, Pavel Pořízka, and Jozef Kaiser 9.1 Introduction and Scope 213 9.2 Artificial Neural Networks (ANNs) 214 9.3 Cost Functions and Training 216 9.4 Backpropagation 219 9.5 Convolutional Neural Networks 221 9.6 Evaluation and Tuning of ANNs 224 9.7 Regularization 227 9.8 State-of-the-art LIBS Classification Using ANNs 229 9.9 Summary 233 Acknowledgments 234 References 234 10 Data Fusion: LIBS + Raman 241 Beatrice Campanella and Stefano Legnaioli 10.1 Introduction 241 10.2 Data Fusion Background 242 10.3 Data Treatment 244 10.4 Working with Images 245 10.4.1 Vectors Concatenation 246 10.4.2 Vectors Co-addition 246 10.4.3 Vectors Outer Sum 246 10.4.4 Vectors Outer Product 247 10.4.5 Data Analysis 247 10.5 Applications 248 10.6 Conclusion 253 References 253 Part IV Quantitative Analysis 257 11 Univariate Linear Methods 259 Stefano Legnaioli, Asia Botto, Beatrice Campanella, Francesco Poggialini, Simona Raneri, and Vincenzo Palleschi 11.1 Standards 259 11.2 Matrix Effect 260 11.3 Normalization 261 11.4 Linear vs. Nonlinear Calibration Curves 264 11.5 Figures of Merit of a Calibration Curve 267 11.5.1 Coefficient of Determination 270 11.5.2 Root Mean Squared Error of Calibration 270 11.5.3 Limit of Detection 270 11.6 Inverse Calibration 273 11.7 Conclusion 274 References 274 12 Partial Least Squares 277 Zongyu Hou, Weiran Song, and Zhe Wang 12.1 Overview 277 12.2 Partial Least Squares Regression Algorithms 278 12.2.1 Nonlinear Iterative PLS 278 12.2.2 SIMPLS Algorithm 279 12.2.3 Kernel Partial Least Squares 279 12.2.4 Locally Weighted Partial Least Squares 280 12.2.5 Dominant Factor-based Partial Least Squares 281 12.3 Partial Least Squares Discriminant Analysis 282 12.4 Results of Partial Least Squares in LIBS 283 12.4.1 Coal Analysis 283 12.4.2 Metal Analysis 285 12.4.3 Rocks, Soils, and Minerals Analysis 285 12.4.4 Organics Analysis 291 12.5 Conclusion 291 References 295 13 Nonlinear Methods 303 Francesco Poggialini, Asia Botto, Beatrice Campanella, Stefano Legnaioli, Simona Raneri, and Vincenzo Palleschi 13.1 Introduction 303 13.2 Multivariate Nonlinear Algorithms 304 13.2.1 Artificial Neural Networks 304 13.2.1.1 Conventional Artificial Neural Networks 304 13.2.1.2 Convolutional Neural Networks 310 13.2.2 Other Nonlinear Multivariate Approaches 312 13.2.2.1 The Franzini–Leoni Method 312 13.2.2.2 The Kalman Filter Approach 313 13.2.2.3 Calibration-Free Methods 314 13.3 Conclusion 315 References 316 14 Laser Ablation-based Techniques – Data Fusion 321 Jhanis Gonzalez 14.1 Introduction 321 14.2 Data Fusion of Multiple Analytical Techniques 322 14.2.1 Low-level Fusion 322 14.2.2 Mid-level Fusion 323 14.2.3 High-level Fusion 324 14.3 Data Fusion of Laser Ablation-Based Techniques 324 14.3.1 Introduction 324 14.3.2 Classification of Edible Salts 326 14.3.2.1 LIBS and LA-ICP-MS Measurements of the Salt Samples 327 14.3.2.2 Mid-Level Data Fusion of LIBS and LA-ICP-MS of Salt Samples 327 14.3.2.3 PLS-DA Classification Model for Salt Samples 333 14.3.3 Coal Discrimination Analysis 334 14.3.3.1 LIBS and LA-ICP-TOF-MS Measurements of the Coal Samples 335 14.3.3.2 Mid-Level Data Fusion of LIBS and LA-ICP-TOF-MS of Coal Samples 335 14.3.3.3 PCA Combined with K-means Cluster Analysis for Coal Samples 338 14.3.3.4 PLS-DA and SVM for Coal Samples Analysis 340 14.4 Comments and Future Developments 341 Acknowledgments 343 References 343 Part V Conclusions 347 15 Conclusion 349 Vincenzo Palleschi Index 351