Czech

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1. Introduction to analysis of multidimentional biological data. Multidimentional analysis object, pros and cons. Classification of the methods.
2. Linear algebra foundations.
3. Multidimentional distributions and statistical tests.
4. Methods for data preprocessing. Transformation and standardization approaches. Problem of missing data.
5. Relationship between variables in multidimentional space. Similarity and distance measures. Correlation and covariance.
6. Cluster analysis of biological data. Hierarchical and non-hierarchical clustering. Determining the optimal number of clusters. Clusters validation.
7. Ordinal analysis. Review of the methods used in biomedical applications.
8. Principal component analysis (PCA). Singular value decomposition.
9. Factor analysis. Fundamentals of factor analysis. Rotation of the factors.
10. Independent component analysis (ICA). ICA based feature extraction from biomedical data. Relationship between PCA, ICA and factor analysis.
11. Non-linear methods for data dimensionality reduction.
12. Multidimensional data analysis in biomedicine applications – overview.

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D. Haruštiaková, J. Jarkovský, S. Littnerová, L. Dušek: Vícerozměrné statistické metody v biologii, CERM 2012 (CS)
J. Holčík: Analýza a klasifikace dat, CERM 2012 (CS)
M. Meloun, J. Militký: Kompendium statistického zpracování dat, Academia 2006 (CS)
Meloun M. a kol.: Statistická analýza vícerozměrných dat v příkladech, 2017, Karolinum, 978-80-246-3618-4

A. Hyvärinen, J. Karhunen, E. Oja: Independent Component Analysis, Wiley 2001 (CS)
M. Kovár: Maticový a tenzorový počet, VUT v Brně (CS)