Chemometrics

FOO-TIM CHAU, PhD, is a Professor in the Department of Applied Biology and Chemical Technology at Hong Kong Polytechnic University. YI-ZENG LIANG, PhD, is a Professor in the College of Chemistry and Chemical Engineering at Central South University, China.JUNBIN GAO, PhD, is a Professor in the Department of Mathematics at Huazhong University of Science and Technology. He is currently visiting the University of Southhampton.XUE-GUANG SHAO, PhD, is a Professor at the University of Science and Technology in China.

"Statisticians, biochemists, engineers, and health researchers will benefit a lot from this wonderful book." (Journal of Statistical Computation and Simulation, November 2005) "...quite useful for persons who apply signal processing methods in chemistry." (Technometrics, May 2005)"…my overall impression of the text is favorable…I would recommend this book to chemists who are interested in using wavelets in their research and to faculty…" (Journal of the American Chemical Society, February 23, 2005)"I recommend this book to chemists who are interested in using wavelets in their research and to faculty who would like to teach graduate students about signal processing..." (Analytical Chemistry, February 1, 2005)"The presentation of information makes it easy for reader to find the relevant information. The text is well-written and understandable." (E-STREAMS, October 2004)

• Preface xiiiChapter 1 Introduction 11.1. Modern Analytical Chemistry 11.1.1. Developments in Modern Chemistry 11.1.2. Modern Analytical Chemistry 21.1.3. Multidimensional Dataset 31.2. Chemometrics 51.2.1. Introduction to Chemometrics 51.2.2. Instrumental Response and Data Processing 81.2.3. White, Black, and Gray Systems 91.3. Chemometrics-Based Signal Processing Techniques 101.3.1. Common Methods for Processing Chemical Data 101.3.2. Wavelets in Chemistry 111.4. Resources Available on Chemometrics and Wavelet Transform 121.4.1. Books 121.4.2. Online Resources 141.4.3. Mathematics Software 15Chapter 2 One-dimensional Signal Processing Techniques in Chemistry 232.1. Digital Smoothing and Filtering Methods 232.1.1. Moving-Window Average Smoothing Method 242.1.2. Savitsky-Golay Filter 252.1.3. Kalman Filtering 322.1.4. Spline Smoothing 362.2. Transformation Methods of Analytical Signals 392.2.1. Physical Meaning of the Convolution Algorithm 392.2.2. Multichannel Advantage in Spectroscopy and Hadamard Transformation 412.2.3. Fourier Transformation 442.2.3.1. Discrete Fourier Transformation and Spectral Multiplex Advantage 452.2.3.2. Fast Fourier Transformation 482.2.3.3. Fourier Transformation as Applied to Smooth Analytical Signals 502.2.3.4. Fourier Transformation as Applied to Convolution and Deconvolution 522.3. Numerical Differentiation 542.3.1. Simple Difference Method 542.3.2. Moving-Window Polynomial Least-Squares Fitting Method 552.4. Data Compression 572.4.1. Data Compression Based on B-Spline Curve Fitting 572.4.2. Data Compression Based on Fourier Transformation 642.4.3. Data Compression Based on Principal-Component Analysis 64Chapter 3 Two-dimensional Signal Processing Techniques in Chemistry 693.1. General Features of Two-Dimensional Data 693.2. Some Basic Concepts for Two-Dimensional Data from Hyphenated Instrumentation 703.2.1. Chemical Rank and Principal-Component Analysis (PCA) 713.2.2. Zero-Component Regions and Estimation of Noise Level and Background 753.3. Double-Centering Technique for Background Correction 773.4. Congruence Analysis and Least-Squares Fitting 783.5. Differentiation Methods for Two-Dimensional Data 803.6 Resolution Methods for Two-Dimensional Data 813.6.1. Local Principal-Component Analysis and Rankmap 833.6.2. Self-Modeling Curve Resolution and Evolving Resolution Methods 853.6.2.1. Evolving Factor Analysis (EFA) 883.6.2.2. Window Factor Analysis (WFA) 903.6.2.3. Heuristic Evolving Latent Projections (HELP) 94Chapter 4 Fundamentals of Wavelet Transform 994.1. Introduction to Wavelet Transform and Wavelet Packet Transform 1004.1.1. A Simple Example: Haar Wavelet 1034.1.2. Multiresolution Signal Decomposition 1084.1.3. Basic Properties of Wavelet Function 1124.2. Wavelet Function Examples 1134.2.1. Meyer Wavelet 1134.2.2. B-Spline (Battle--Lemarié) Wavelets 1144.2.3. Daubechies Wavelets 1164.2.4. Coiflet Functions 1174.3. Fast Wavelet Algorithm and Packet Algorithm 1184.3.1. Fast Wavelet Transform 1194.3.2. Inverse Fast Wavelet Transform 1224.3.3. Finite Discrete Signal Handling with Wavelet Transform 1254.3.4. Packet Wavelet Transform 1324.4. Biorthogonal Wavelet Transform 1344.4.1. Multiresolution Signal Decomposition of Biorthogonal Wavelet 1344.4.2. Biorthogonal Spline Wavelets 1364.4.3. A Computing Example 1374.5. Two-Dimensional Wavelet Transform 1404.5.1. Multidimensional Wavelet Analysis 1404.5.2. Implementation of Two-Dimensional Wavelet Transform 141Chapter 5 Application of Wavelet Transform In Chemistry 1475.1. Data Compression 1485.1.1. Principle and Algorithm 1495.1.2. Data Compression Using Wavelet Packet Transform 1555.1.3. Best-Basis Selection and Criteria for Coefficient Selection 1585.2. Data Denoising and Smoothing 1665.2.1. Denoising 1675.2.2. Smoothing 1735.2.3. Denoising and Smoothing Using Wavelet Packet Transform 1795.2.4. Comparison between Wavelet Transform and Conventional Methods 1825.3. Baseline/Background Removal 1835.3.1. Principle and Algorithm 1845.3.2. Background Removal 1855.3.3. Baseline Correction 1915.3.4. Background Removal Using Continuous Wavelet Transform 1915.3.5. Background Removal of Two-Dimensional Signals 1965.4. Resolution Enhancement 1995.4.1. Numerical Differentiation Using Discrete Wavelet Transform 2005.4.2. Numerical Differentiation Using Continuous Wavelet Transform 2055.4.3. Comparison between Wavelet Transform and other Numerical Differentiation Methods 2105.4.4. Resolution Enhancement 2125.4.5. Resolution Enhancement by Using Wavelet Packet Transform 2205.4.6. Comparison between Wavelet Transform and Fast Fourier Transform for Resolution Enhancement 2215.5. Combined Techniques 2255.5.1. Combined Method for Regression and Calibration 2255.5.2. Combined Method for Classification and Pattern Recognition 2275.5.3. Combined Method of Wavelet Transform and Chemical Factor Analysis 2285.5.4. Wavelet Neural Network 2305.6. An Overview of the Applications in Chemistry 2325.6.1. Flow Injection Analysis 2335.6.2. Chromatography and Capillary Electrophoresis 2345.6.3. Spectroscopy 2385.6.4. Electrochemistry 2445.6.5. Mass Spectrometry 2465.6.6. Chemical Physics and Quantum Chemistry 2485.6.7. Conclusion 249Appendix Vector and Matrix Operations and Elementary MATLAB 257A.1. Elementary Knowledge in Linear Algebra 257A.1.1. Vectors and Matrices in Analytical Chemistry 257A.1.2. Column and Row Vectors 259A.1.3. Addition and Subtraction of Vectors 259A.1.4. Vector Direction and Length 260A.1.5. Scalar Multiplication of Vectors 261A.1.6. Inner and Outer Products between Vectors 262A.1.7. The Matrix and Its Operations 263A.1.8. Matrix Addition and Subtraction 264A.1.9. Matrix Multiplication 264A.1.10. Zero Matrix and Identity Matrix 264A.1.11. Transpose of a Matrix 265A.1.12. Determinant of a Matrix 265A.1.13. Inverse of a Matrix 266A.1.14. Orthogonal Matrix 266A.1.15. Trace of a Square Matrix 267A.1.16. Rank of a Matrix 268A.1.17. Eigenvalues and Eigenvectors of a Matrix 268A.1.18. Singular-Value Decomposition 269A.1.19. Generalized Inverse 270A.1.20. Derivative of a Matrix 271A.1.21. Derivative of a Function with Vector as Variable 271A.2. Elementary Knowledge of MATLAB 273A.2.1. Matrix Construction 275A.2.2. Matrix Manipulation 275A.2.3. Basic Mathematical Functions 276A.2.4. Methods for Generating Vectors and Matrices 278A.2.5. Matrix Subscript System 280A.2.6. Matrix Decomposition 286A.2.6.1. Singular-Value Decomposition (SVD) 286A.2.6.2. Eigenvalues and Eigenvectors (eig) 287A.2.7. Graphic Functions 288Index 293