Alexey L. Pomerantsev

Chemometrics in Excel (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Providing an easy explanation of the fundamentals, methods, and applications of chemometrics * Acts as a practical guide to multivariate data analysis techniques * Explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations * Presents the basic chemometric methods as worksheet functions in Excel * Includes Chemometrics Add In for download which uses Microsoft Excel® for chemometrics training * Online downloads includes workbooks with examples

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 336
• Erscheinungstermin: 6. Mai 2014
• Englisch
• ISBN-13: 9781118873267
• Artikelnr.: 41047343

Autorenporträt

Alexey L Pomerantsev is a Leading Researcher at The Russian Academy of Science. He is a founding member and Chair of the Russian Chemometrics Society, being instrumental in organizing the annual Winter Symposium on Chemometrics. He is a peer reviewer and member of Editorial Board of the Journal 'Chemometrics and Intelligent Laboratory Systems.' Dr. Pomerantsev has over 100 publications, many of them dealing with Chemometric Investigations.

Inhaltsangabe

Preface xvii PART I INTRODUCTION 1 1 What is Chemometrics? 3 1.1 Subject of Chemometrics
3 1.2 Historical Digression
5 2 What the Book Is About? 8 2.1 Useful Hints
8 2.2 Book Syllabus
9 2.3 Notations
10 3 Installation of Chemometrics Add-In 11 3.1 Installation
11 3.2 General Information
14 4 Further Reading on Chemometrics 15 4.1 Books
15 4.1.1 The Basics
15 4.1.2 Chemometrics
16 4.1.3 Supplements
16 4.2 The Internet
17 4.2.1 Tutorials
17 4.3 Journals
17 4.3.1 Chemometrics
17 4.3.2 Analytical
18 4.3.3 Mathematical
18 4.4 Software
18 4.4.1 Specialized Packages
18 4.4.2 General Statistic Packages
19 4.4.3 Free Ware
19 PART II THE BASICS 21 5 Matrices and Vectors 23 5.1 The Basics
23 5.1.1 Matrix
23 5.1.2 Simple Matrix Operations
24 5.1.3 Matrices Multiplication
25 5.1.4 Square Matrix
26 5.1.5 Trace and Determinant
27 5.1.6 Vectors
28 5.1.7 Simple Vector Operations
29 5.1.8 Vector Products
29 5.1.9 Vector Norm
30 5.1.10 Angle Between Vectors
30 5.1.11 Vector Representation of a Matrix
30 5.1.12 Linearly Dependent Vectors
31 5.1.13 Matrix Rank
31 5.1.14 Inverse Matrix
31 5.1.15 Pseudoinverse
32 5.1.16 Matrix-Vector Product
33 5.2 Advanced Information
33 5.2.1 Systems of Linear Equations
33 5.2.2 Bilinear and Quadratic Forms
34 5.2.3 Positive Definite Matrix
34 5.2.4 Cholesky Decomposition
34 5.2.5 Polar Decomposition
34 5.2.6 Eigenvalues and Eigenvectors
35 5.2.7 Eigenvalues
35 5.2.8 Eigenvectors
35 5.2.9 Equivalence and Similarity
36 5.2.10 Diagonalization
37 5.2.11 Singular Value Decomposition (SVD)
37 5.2.12 Vector Space
38 5.2.13 Space Basis
39 5.2.14 Geometric Interpretation
39 5.2.15 Nonuniqueness of Basis
39 5.2.16 Subspace
40 5.2.17 Projection
40 6 Statistics 42 6.1 The Basics
42 6.1.1 Probability
42 6.1.2 Random Value
43 6.1.3 Distribution Function
43 6.1.4 Mathematical Expectation
44 6.1.5 Variance and Standard Deviation
44 6.1.6 Moments
44 6.1.7 Quantiles
45 6.1.8 Multivariate Distributions
45 6.1.9 Covariance and Correlation
45 6.1.10 Function
46 6.1.11 Standardization
46 6.2 Main Distributions
46 6.2.1 Binomial Distribution
46 6.2.2 Uniform Distribution
47 6.2.3 Normal Distribution
48 6.2.4 Chi-Squared Distribution
50 6.2.5 Student's Distribution
52 6.2.6 F-Distribution
53 6.2.7 Multivariate Normal Distribution
54 6.2.8 Pseudorandom Numbers
55 6.3 Parameter Estimation
56 6.3.1 Sample
56 6.3.2 Outliers and Extremes
56 6.3.3 Statistical Population
56 6.3.4 Statistics
57 6.3.5 Sample Mean and Variance
57 6.3.6 Sample Covariance and Correlation
58 6.3.7 Order Statistics
59 6.3.8 Empirical Distribution and Histogram
60 6.3.9 Method of Moments
61 6.3.10 The Maximum Likelihood Method
62 6.4 Properties of the Estimators
62 6.4.1 Consistency
62 6.4.2 Bias
63 6.4.3 Effectiveness
63 6.4.4 Robustness
63 6.4.5 Normal Sample
64 6.5 Confidence Estimation
64 6.5.1 Confidence Region
64 6.5.2 Confidence Interval
65 6.5.3 Example of a Confidence Interval
65 6.5.4 Confidence Intervals for the Normal Distribution
65 6.6 Hypothesis Testing
66 6.6.1 Hypothesis
66 6.6.2 Hypothesis Testing
66 6.6.3 Type I and Type II Errors
67 6.6.4 Example
67 6.6.5 Pearson's Chi-Squared Test
67 6.6.6 F-Test
69 6.7 Regression
70 6.7.1 Simple Regression
70 6.7.2 The Least Squares Method
71 6.7.3 Multiple Regression
72 Conclusion
73 7 Matrix Calculations in Excel 74 7.1 Basic Information
74 7.1.1 Region and Language
74 7.1.2 Workbook
Worksheet
and Cell
76 7.1.3 Addressing
77 7.1.4 Range
78 7.1.5 Simple Calculations
78 7.1.6 Functions
78 7.1.7 Important Functions
81 7.1.8 Errors in Formulas
85 7.1.9 Formula Dragging
86 7.1.10 Create a Chart
87 7.2 Matrix Operations
88 7.2.1 Array Formulas
88 7.2.2 Creating and Editing an Array Formula
90 7.2.3 Simplest Matrix Operations
91 7.2.4 Access to the Part of a Matrix
91 7.2.5 Unary Operations
93 7.2.6 Binary Operations
95 7.2.7 Regression
95 7.2.8 Critical Bug in Excel 2003
99 7.2.9 Virtual Array
99 7.3 Extension of Excel Possibilities
100 7.3.1 VBA Programming
100 7.3.2 Example
101 7.3.3 Macro Example
103 7.3.4 User-Defined Function Example
104 7.3.5 Add-Ins
105 7.3.6 Add-In Installation
106 Conclusion
107 8 Projection Methods in Excel 108 8.1 Projection Methods
108 8.1.1 Concept and Notation
108 8.1.2 PCA
109 8.1.3 PLS
110 8.1.4 Data Preprocessing
111 8.1.5 Didactic Example
112 8.2 Application of Chemometrics Add-In
113 8.2.1 Installation
113 8.2.2 General
113 8.3 PCA
114 8.3.1 ScoresPCA
114 8.3.2 LoadingsPCA
114 8.4 PLS
116 8.4.1 ScoresPLS
116 8.4.2 UScoresPLS
117 8.4.3 LoadingsPLS
118 8.4.4 WLoadingsPLS
119 8.4.5 QLoadingsPLS
120 8.5 PLS2
121 8.5.1 ScoresPLS2
121 8.5.2 UScoresPLS2
122 8.5.3 LoadingsPLS2
124 8.5.4 WLoadingsPLS2
125 8.5.5 QLoadingsPLS2
126 8.6 Additional Functions
127 8.6.1 MIdent
127 8.6.2 MIdentD2
127 8.6.3 MCutRows
129 8.6.4 MTrace
129 Conclusion
130 PART IIICHEMOMETRICS 131 9 Principal Component Analysis (PCA) 133 9.1 The Basics
133 9.1.1 Data
133 9.1.2 Intuitive Approach
134 9.1.3 Dimensionality Reduction
136 9.2 Principal Component Analysis
136 9.2.1 Formal Specifications
136 9.2.2 Algorithm
137 9.2.3 PCA and SVD
137 9.2.4 Scores
138 9.2.5 Loadings
139 9.2.6 Data of Special Kind
140 9.2.7 Errors
140 9.2.8 Validation
143 9.2.9 Decomposition "Quality"
143 9.2.10 Number of Principal Components
144 9.2.11 The Ambiguity of PCA
145 9.2.12 Data Preprocessing
146 9.2.13 Leverage and Deviation
146 9.3 People and Countries
146 9.3.1 Example
146 9.3.2 Data
147 9.3.3 Data Exploration
147 9.3.4 Data Pretreatment
148 9.3.5 Scores and Loadings Calculation
149 9.3.6 Scores Plots
151 9.3.7 Loadings Plot
152 9.3.8 Analysis of Residuals
153 Conclusion
153 10 Calibration 156 10.1 The Basics
156 10.1.1 Problem Statement
156 10.1.2 Linear and Nonlinear Calibration
157 10.1.3 Calibration and Validation
158 10.1.4 Calibration "Quality"
160 10.1.5 Uncertainty
Precision
and Accuracy
162 10.1.6 Underfitting and Overfitting
163 10.1.7 Multicollinearity
164 10.1.8 Data Preprocessing
166 10.2 Simulated Data
166 10.2.1 The Principle of Linearity
166 10.2.2 "Pure" Spectra
166 10.2.3 "Standard" Samples
166 10.2.4 X Data Creation
167 10.2.5 Data Centering
168 10.2.6 Data Overview
168 10.3 Classic Calibration
169 10.3.1 Univariate (Single Channel) Calibration
169 10.3.2 The Vierordt Method
172 10.3.3 Indirect Calibration
174 10.4 Inverse Calibration
176 10.4.1 Multiple Linear Calibration
177 10.4.2 Stepwise Calibration
178 10.5 Latent Variables Calibration
180 10.5.1 Projection Methods
180 10.5.2 Latent Variables Regression
184 10.5.3 Implementation of Latent Variable Calibration
185 10.5.4 Principal Component Regression (PCR)
186 10.5.5 Projection on the Latent Structures-1 (PLS1)
188 10.5.6 Projection on the Latent Structures-2 (PLS2)
191 10.6 Methods Comparison
193 Conclusion
197 11 Classification 198 11.1 The Basics
198 11.1.1 Problem Statement
198 11.1.2 Types of Classes
199 11.1.3 Hypothesis Testing
199 11.1.4 Errors in Classification
200 11.1.5 One-Class Classification
200 11.1.6 Training and Validation
201 11.1.7 Supervised and Unsupervised Training
201 11.1.8 The Curse of Dimensionality
201 11.1.9 Data Preprocessing
201 11.2 Data
202 11.2.1 Example
202 11.2.2 Data Subsets
203 11.2.3 Workbook Iris.xls
204 11.2.4 Principal Component Analysis
205 11.3 Supervised Classification
205 11.3.1 Linear Discriminant Analysis (LDA)
205 11.3.2 Quadratic Discriminant Analysis (QDA)
210 11.3.3 PLS Discriminant Analysis (PLSDA)
214 11.3.4 SIMCA
217 11.3.5 k-Nearest Neighbors (kNN)
223 11.4 Unsupervised Classification
225 11.4.1 PCA Again (Revisited)
225 11.4.2 Clustering by K-Means
225 Conclusion
229 12 Multivariate Curve Resolution 230 12.1 The Basics
230 12.1.1 Problem Statement
230 12.1.2 Solution Ambiguity
232 12.1.3 Solvability Conditions
234 12.1.4 Two Types of Data
235 12.1.5 Known Spectrum or Profile
236 12.1.6 Principal Component Analysis (PCA)
236 12.1.7 PCA and MCR
237 12.2 Simulated Data
237 12.2.1 Example
237 12.2.2 Data
238 12.2.3 PCA
238 12.2.4 The HELP Plot
240 12.3 Factor Analysis
241 12.3.1 Procrustes Analysis
241 12.3.2 Evolving Factor Analysis (EFA)
244 12.3.3 Windows Factor Analysis (WFA)
246 12.4 Iterative Methods
249 12.4.1 Iterative Target Transform Factor Analysis (ITTFA)
249 12.4.2 Alternating Least Squares (ALS)
250 Conclusion
252 PART IV SUPPLEMENTS 255 13 Extension Of Chemometrics Add-In 257 13.1 Using Virtual Arrays
257 13.1.1 Simulated Data
257 13.1.2 Virtual Array
259 13.1.3 Data Preprocessing
259 13.1.4 Decomposition
260 13.1.5 Residuals Calculation
260 13.1.6 Eigenvalues Calculation
262 13.1.7 Orthogonal Distances Calculation
263 13.1.8 Leverages Calculation
264 13.2 Using VBA Programming
265 13.2.1 VBA Advantages
265 13.2.2 Virtualization of Real Arrays
265 13.2.3 Data Preprocessing
266 13.2.4 Residuals Calculation
267 13.2.5 Eigenvalues Calculation
268 13.2.6 Orthogonal Distances Calculation
269 13.2.7 Leverages Calculation
270 Conclusion
271 14 Kinetic Modeling of Spectral Data 272 14.1 The "Grey" Modeling Method
272 14.1.1 Problem Statement
272 14.1.2 Example
274 14.1.3 Data
274 14.1.4 Soft Method of Alternating Least Squares (Soft-ALS)
275 14.1.5 Hard Method of Alternating Least Squares (Hard-ALS)
277 14.1.6 Using Solver Add-In
279 Conclusions
282 15 MATLAB(r): Beginner's Guide 283 15.1 The Basics
283 15.1.1 Workspace
283 15.1.2 Basic Calculations
285 15.1.3 Echo
285 15.1.4 Workspace Saving: MAT-Files
286 15.1.5 Diary
286 15.1.6 Help
287 15.2 Matrices
287 15.2.1 Scalars
Vectors
and Matrices
287 15.2.2 Accessing Matrix Elements
289 15.2.3 Basic Matrix Operations
289 15.2.4 Special Matrices
290 15.2.5 Matrix Calculations
292 15.3 Integrating Excel and MATLAB(r)
294 15.3.1 Configuring Excel
294 15.3.2 Data Exchange
294 15.4 Programming
295 15.4.1 M-Files
295 15.4.2 Script File
296 15.4.3 Function File
297 15.4.4 Plotting
298 15.4.5 Plot Printing
300 15.5 Sample Programs
301 15.5.1 Centering and Scaling
301 15.5.2 SVD/PCA
301 15.5.3 PCA/NIPALS
302 15.5.4 PLS1
303 15.5.5 PLS2
304 Conclusion
306 Afterword. The Fourth Paradigm 307 Index 311