Handbook of Chemometrics and Qualimetrics

Introduction to Part B. Vectors, Matrices and Operations on Matrices. Vector space. Geometrical properties of vectors. Matrices. Matrix product. Dimensions and rank. Eigenvectors and eigenvalues. Statistical interpretation of matrices. Geometrical interpretation of matrix products. References. Cluster Analysis. Clusters. Measures of (dis)similarity. Clustering algorithms. References. Analysis of Measurement Tables. Introduction. Principal components analysis. Geometrical interpretation. Preprocessing. Algorithms. Validation. Principal coordinates analysis. Non-linear principal components analysis. PCA and cluster analysis. References. Analysis of Contingency Tables. Contingency table. Chi-square statistic. Closure. Weighted metric. Distance of chi-square. Correspondence factor analysis. Log-linear model. References. Supervised Pattern Recognition. Supervised and unsupervised pattern recognition. Derivation of classification rules. Feature of selection and reduction. Validation of classification rules. References. Curve and Mixture Resolution by Factor Analysis and Related Techniques. Abstract and true factors. Full-rank methods. Evolutionary and local rank methods. Pure column (or row) techniques. Quantitative methods for factor analysis. Application of factor analysis for peak purity check in HPLC. Guidance for the selection of a factor analysis method. References. Relations between Measurement Tables. Introduction. Procrustes analysis. Canonical correlation analysis. Multivariate least squares regression. Reduced rank regression. Partial least squares regression. Continuum regression methods. Concluding remarks. References. Multivariate Calibration. Introduction. Calibration methods. Validation. Other aspects. New developments. References. Quantitative Structure-Activity Relationships (QSAR). Extrathermodynamic methods. Principal components models. Canonical variate models. Partial least squares models. Other approaches. References. Analysis of Sensory Data. Introduction. Difference tests. Multidimensional scaling. The analysis of Quantitative Descriptive Analysis profile data. Comparison of two or more sensory data sets. Linking sensory data to instrumental data. Temporal aspects of perception. Production formulation. References. Pharmacokinetic Models. Introduction. Compartmental analysis. Non-compartmental analysis. Compartment models versus non-compartmental analysis. Linearization of non-linear models. References. Signal Processing. Signal domains. Types of signal processing. The Fourier transform. Convolution. Signal processing. Deconvolution by Fourier transform. Other transforms. References. Kalman Filtering. Introduction. Recursive regression of a straight line. Recursive multicomponent analysis. System equations. The Kalman filter. Adaptive Kalman filtering. Applications. References. Applications of Operations Research. An overview. Linear programming. Queueing problems. Discrete event simulation. A shortest path problem. References. Artificial Intelligence: Expert and Knowledge Based Systems. Artificial intelligence and expert systems. Expert systems. Structure of expert systems. Knowledge representation. The interference engine. The interaction module. Tools. Developments of an expert system. Conclusion. References. Artificial Neural Networks. Introduction. Historical overview. The basic unit - the neuron. The linear learning machine and the perception network. Multilayer feed forward (MLF) networks. Radial basis function networks. Kohonen networks. Adaptive resonance theory networks. References.