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This course focuses on statistical methods based on matrix computations where the effective application of methods of numerical linear algebra is crucial. The main emphasis is on understanding and selecting methods that have low computational and memory requirements, and are if possible stable and reliable.
The first part of the course will concentrate on statistical tasks associated with the matrix decomposition SVD, like PCA, regression, dimension reduction and the small sample size problem (especially in the case of sparse data), pattern recognition and similar classification tasks or problems from the area of data mining. In the next part we will focus on non-negative matrix decompositions used for example in text mining and on computations of numerical linear algebra that are used to solve the page ranking problem for search engines.
Last update: Duintjer Tebbens Erik Jurjen, doc. Dipl.-Math., Ph.D. (14.09.2013)
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The credit test consists of succesful implementation of an exercise in Matlab. The exercise is similar to what has been done during the regular exercises of the course.
Last update: Duintjer Tebbens Erik Jurjen, doc. Dipl.-Math., Ph.D. (30.05.2018)
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ELDEN, L.: Matrix Methods in Data Mining and Pattern Recognition, Fundamentals of Algorithms, 4. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007.
BJORCK, ÅKE: Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996.
HIGHAM, N., STEWART, G. W.: Numerical Linear Algebra in Statistical Computing. The state of the art in numerical analysis (Birmingham, 1986), Inst. Math. Appl. Conf. Ser. New Ser., 9, Oxford Univ. Press, New York, 1987, pp. 41-57.
DUINTJER TEBBENS, J., SCHLESINGER, P.: Improving Implementation of Linear Discriminant Analysis for the High Dimension/Small Sample Size Problem, Computational Statistics and Data Analysis, 2007, vol. 52, no.1, pp. 423-437.
J. KALINA, J. DUINTJER TEBBENS: Metody pro redukci dimenze v mnohorozměrné statistice a jejich výpočet, to appear in the Informacní bulletin of the Czech Statistical Society, in 2014.
J. DUINTJER TEBBENS, I. HNĚTYNKOVÁ, M. PLEŠINGER, Z. STRAKOŠ and P. TICHÝ: Analysis of Methods for Matrix Computations, Basic Methods (in Czech), Matfyzpress Prague, ISBN 978-80-7378-201-6, first edition, 2012, 328 pp.
Last update: Kučera Václav, doc. RNDr., Ph.D. (15.01.2019)
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Lecture+exercises. Last update: T_KPMS (12.05.2014)
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The exam is written with most questions multiple-choice questions, except for one or two requiring detailed descriptions. All lectured material will be examinated from.
Last update: Duintjer Tebbens Erik Jurjen, doc. Dipl.-Math., Ph.D. (30.05.2018)
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1. Numerical properties of the SVD and spectral decomposition.
2. PCA and the spectral decomposition.
3. (Multi)-linear regression and the SVD.
4. Dimension reduction in high-dimensional statistics.
5. Pattern recognition and other classification tasks.
6. Nonnegative matrix decompositions.
7. The page ranking problem. Last update: Kučera Václav, doc. RNDr., Ph.D. (19.12.2018)
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Only very basic knowledge of linear algebra is required - further knowledge, in particular concerning numerics, is lectured during the course. Last update: Duintjer Tebbens Erik Jurjen, doc. Dipl.-Math., Ph.D. (30.05.2018)
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