Multivariate Pattern Recognition in Chemometrics : Illustrated by Case Studies
, by Brereton, Richard G.Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
- ISBN: 9780444897831 | 0444897836
- Cover: Hardcover
- Copyright: 9/1/1992
Acknowledgements | |
Contributors | |
Introduction | p. 1 |
References | p. 4 |
Introduction to Multivariate Space | |
Introduction | p. 7 |
Matrices | p. 7 |
Multivariate space | p. 10 |
Dimension and rank | p. 12 |
Matrix product | p. 13 |
Vectors as one-dimensional matrices | p. 16 |
Unit matrix as a frame of multivariate space | p. 17 |
Product of a matrix with a vector. Projection of points upon a single axis | p. 18 |
Multiple linear regression (MLR) as a projection of points upon an axis | p. 20 |
Linear discriminant analysis (LDA) as a projection of points on an axis | p. 23 |
Product of a matrix with a two-column matrix. Projection of points upon a plane | p. 25 |
Product of two matrices as a rotation of points in multivariate space | p. 26 |
Factor rotation | p. 30 |
Factor data analysis | p. 34 |
References | p. 36 |
Answers | p. 37 |
Multivariate Data Display | |
Introduction | p. 43 |
Basic methods of factor data analysis | p. 44 |
Choice of a particular display method | p. 46 |
SPECTRAMAP program | p. 51 |
The neuroleptics case | p. 54 |
Principal components analysis (PCA) with standardization | p. 56 |
Principal components analysis (PCA) with logarithms | p. 59 |
Correspondence factor analysis (CFA) | p. 63 |
Spectral map analysis (SMA) | p. 64 |
References | p. 66 |
Answers | p. 67 |
Vectors and Matrices : Basic Matrix Algebra | |
Introduction | p. 71 |
The data matrix | p. 71 |
Vector representation | p. 74 |
Vector manipulation | p. 78 |
Matrices | p. 82 |
Statistical equivalents | p. 89 |
References | p. 91 |
Answers | p. 92 |
The Mathematics of Pattern Recognition | |
Introduction | p. 99 |
Rotation and projection | p. 99 |
Dimensionality | p. 103 |
Expressing the information in the data | p. 112 |
Decomposition of data | p. 116 |
Final comments | p. 120 |
References | p. 121 |
Answers | p. 122 |
Data Reduction Using Principal Components Analysis | |
Introduction | p. 125 |
Principal components analysis | p. 126 |
Data reduction by dimensionality reduction | p. 131 |
Data reduction by variable reduction | p. 150 |
Conclusions | p. 164 |
References | p. 165 |
Answers | p. 167 |
Cluster Analysis | |
Introduction | p. 179 |
Two problems | p. 180 |
Visual inspection | p. 183 |
Measurement of distance and similarity | p. 183 |
Hierarchical methods | p. 190 |
Optimization partitioning methods | p. 197 |
Conclusions | p. 204 |
References | p. 204 |
Answers | p. 205 |
SIMCA - Classification by Means of Disjoint Cross Validated Principal Components Models | |
Introduction | p. 209 |
Distance, variance and covariance | p. 210 |
The principal component model | p. 217 |
Unsupervised principal component modelling | p. 220 |
Supervised principal component modelling using cross-validation | p. 222 |
Cross validated principal component models | p. 222 |
The SIMCA model | p. 226 |
Classification of new samples to a class model | p. 230 |
Communality and modelling power | p. 233 |
Discriminatory ability of variables | p. 235 |
Separation between classes | p. 236 |
Detection of outliers | p. 238 |
Data reduction by means of relevance | p. 240 |
Conclusion | p. 242 |
Acknowledgements | p. 242 |
References | p. 242 |
Answers | p. 245 |
Hard Modelling in Supervised Pattern Recognition | |
Introduction | p. 249 |
The data set | p. 249 |
Geometric representation | p. 252 |
Classification rule | p. 254 |
Deterministic pattern recognition | p. 255 |
Probabilistic pattern recognition | p. 273 |
Final remarks | p. 276 |
References | p. 277 |
Answers | p. 278 |
Software Appendices | |
Spectramap | |
Installation of the program | p. 289 |
Execution of the program | p. 290 |
Tutorial cases | p. 293 |
Sirius | |
Introduction | p. 303 |
Starting SIRIUS | p. 303 |
The data table | p. 304 |
Defining, selecting and storing a class | p. 304 |
Principal component modelling | p. 306 |
Variance decomposition plots and other graphic representations | p. 313 |
Summary | p. 320 |
Acknowledgements | p. 320 |
References | p. 320 |
Index | p. 321 |
Table of Contents provided by Blackwell. All Rights Reserved. |
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