| Multivariate Analysis in Chemistry | |
| Unit Code | ASC 10 |
| Credits | 5 |
| Prerequisites | Eurobachelor in chemistry or equivalent |
| TEACHING STAFF | Prof. Andrzej Parczewski, Dr hab. Andrzej M. Turek, Dr. hab. Małgorzata Barańska |
COURSE DESCRIPTION: Multivariate analysis in chemistry.
PART I: Chemometrics and biometrics: Prof. A. Parczewski
Statistical treatment of experimental data. Introduction to mathematical modeling of processes. Empirical modeling. Linear models: determination of the model parameters
and the corresponding variance-covariance matrix, model adequacy testing. Nonlinear models. Design of experiments. Optimization methods: single factor, gradient,
simplex, Monte Carlo, Genetic Algorithm. Statistical treatment of multidimensional data. Introduction to the Principal Component Analysis (PCA) and Factor Analysis (FA),
Cluster Analysis (CA), Pattern Recognition methods, Artificial Neural Networks (ANN), and other chemometric and biometric methods.
PART II: Factor analysis in chemistry: Dr hab. A. M. Turek
Theoretical aspects and practical applications of Singular Value Decomposition (SVD), Target Factor Analysis (TFA), Evolutionary Rank Analysis (ERA),
non-factor algorithms of spectral analysis (OPA and SIMPLISMA), ordinary and Generalized Rank Annihilation Factor Analyses (RAFA and GRAFA). Comparison between
physically constrained and unconstrained methods of factor analysis curve resolution. Regression models for two-way two-block data analysis: Multiple Linear Regression
(MLR), Principal Component Regression (PCR) and Partial Least Squares (PLS) regression, non-quantitative and Quantitative Structure-Activity Relationships
(SAR and QSAR), multimode factor analysis including 3DRAFA, Alternating Least Squares Multiple Component Resolution (ALS-MCR), the Tucker models and Parallel Factor
Analysis (PARAFAC).
OBJECTIVE OF THE COURSE:
The aims of this unit are:
- To get the student acquainted with the statistical methods of evaluation and processing of various chemical data
- To teach the student how to construct the models of multivariate chemical processes
- To show the student how to extract from the measured spectroscopic data the quantitative relationships
INTENDED LEARNING OUTCOMES:
After completing this course the student should be able to propose and apply different data processing methods in order to retrieve the valuable information from the experimental data
TEACHING AND LEARNING ACTIVITIES:
| TERM | NAME | L | S/E | P |
| 2 | Multivariate Analysis in Chemistry | 30 | 0 | 15 |
| Part I : Chemometry and Biometry | 15 | 0 | 6 | |
| Part II : Factor Analysis in Chemistry | 15 | 0 | 9 |
Student centred learning: 80 hours; total student effort: 125 hours
LANGUAGE OF INSTRUCTION: English
RECOMMENDED READING:
Handbook of Chemometrics and Qualimetrics. Vol 20 A and B: D. L. Massart, B. Vandeginste, L. Buydens, S. De Jong, P. Lewi and Smeyers-Verbeke, (1998), Edition: Elsevier
Factor Analysis in Chemistry, E. R. Malinowski, (2002) 3rd Edition: John Wiley and Sons
Multi-way Analysis., A. Smilde, R. Bro, P. Geladi, (2004), Edition: John Wiley and Sons
Chemometrics in Spectroscopy, H. Mark, J. Workman J., Jr., (2007) Edition: Elsevier Inc.
K. Danzer, Analytical Chemistry. Theoretical and Methodological Fundamentals, (2007), Springer
K. Danzer, H. Hobert, C. Fischbacher, K.-U. Jagemann, Chemometrik. Grundlagen und Anwendungen, (2001), Springer
SCHEDULE AND LEARNING METHOD:
Part I: Chemometrics and Biometrics:
| Weeks | Type | Duration | Course description |
| 1 | L | 1 | The ideas and methods of statistics employed in experimental data handling: general population and sample; estimation of parameters of a random variable distribution; expected (mean) values of random variable functions |
| 2 | L | 1 | Uncertainty of measurement data; confidence interval for µ. Distribution of the Student's t , X2 and F variables |
| 3 | L | 1 | Testing of statistical hypotheses; a general idea and applications |
| 4 | L | 1 | Statistical dependence between random variables; covariance, correlation coefficient and determination coefficient; information redundancy |
| 6 | L P |
1 3 |
Design of experiments. Optimisation of processes in chemistry. Optimisation strategies - a general review |
| 7 | L | 1 | Optimisation methods: single factor, gradient, simplex, Monte Carlo, Genetic Algorithm |
| 8 | L | 1 | Chemometric treatment of multidimensional data. Data matrix and its transformation. Examination of data structure |
| 9 | L | 1 | Measures of similarity between objects and between variables (features) |
| 10 | L | 1 | Cluster Analysis (CA): strategies of clustering. Dendrogram as a means of clusters presentations |
| 11 | L P |
1-3 | Examples of CA application in analytical chemistry, interpretation of environment monitoring data and profiling of drugs |
| 12 | L | 1 | Principal Component Analysis (PCA); an idea of the approach |
| 13 | L | 1 | Examples of PCA application; comparison with CA |
| 14 | L | 1 | Pattern Recognition (PR) approaches; an overview |
| 15 | L | 1 | Artificial Neural Networks (ANN) and other methods of multidimensional data analysis (brief review) |
Part II: Factor Analysis in Chemistry
| Weeks | Type | Duration | Course description |
| 1 | L | 1 | Historical outline. Notation and elementary operations |
| 2 | L | 1 | Examples of factor analysis on non-chemical correlation matrices |
| 3 | L P |
1 3 |
Target factor analysis (TFA) and generalized method of standard addition. Spectrophotometric quantification of three-component system |
| 4 | L | 1 | Evolutionary rank analysis (EFA, FSMW-EFA, HELP with LPGs, one-way and two-way-ETA, cookie-cutter method) |
| 5 | L P |
3 | Non-factor analysis of spectral data (OPA and SIMPLISMA) |
| 6 | L | 1 | Rank annihilation factor analysis (RAFA and RAEFA) |
| 7 | L | 1 | Generalized rank annihilation factor analysis (GRAFA) |
| 8 | L | 1 | Direct exponential curve resolution algorithm (DECRA) |
| 9 | L P |
1 3 |
Comparison of physically constrained and unconstrained methods of factor analysis (PCA-SM-SV versus Kubista's approach). Resolution of two-component fluorescence spectra. |
| 10 | L | 1 | Multimode factor analysis: Three dimensional rank annihilation factor analysis (3DRAFA) and alternating least squares multiple component resolution (ALS-MCR) |
| 11 | L | 1 | Regression models for two-way two-block data analysis: Multiple linear regression (MLR) |
| 12 | L | 1 | Regression models for two-way two-block data analysis: Principal component regression (PCR) and partial least squares (PLS) regression |
| 13 | L P |
1 3 |
Qualitative and quantitative structure activity relationship (SAR and QSAR). QSAR for log CMC |
| 14 | L | 1 | Multimode factor analysis: Tucker models |
| 15 | L | 1 | Multimode factor analysis: Parallel factor analysis |
ASSESSMENT:
Examination on completion of teaching period: written or oral (weighting 100%)