1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
The main objective is development of mathematical modelling techniques and skills for advanced data analysis, e.g.how to extract valuable latent information from a large volume of raw data,
Concrete real-world examples (e.g. Internet search engines, protein structure, image analysis, face recognition, algorithmic character recognition) are used to illustrate how real-world objects and actions can be represented by mathematical objects and operation/functions on them.
It is shown how a sequence of elementary steps yields highly sophisticated mathematical models that combine techniques from statistics, numerical mathematics, graph theory, multilinear algebra etc. In that sense, this course can be considered as practical integral application of mathematical skills to real-world problems, with additional value in mastering modern methods in data analysis, dimension reduction and network analysis.

COURSE DESCRIPTION AND SYLLABUS:
1. Vector models (motivation and examples - text data, digital images, video etc)
2. Clustering methods (k-means and its variations, spectral relaxation)
3. SVD decomposition and applications to dimension reduction, denoising and steganography
4. Clustering using spectral cuts in weighted graphs
5. Google page rang algorithm with analysis using the theory of nonnegative and stochastic matrices
6. Centrality and other similarity measures in weighted graphs
7. Tensors and tensor decompositions
8. Tensor SVD and tensor compression with applications
9. Nonnegative matrix factorisations with applications to clustering
10. Case studies

1. The 25,000,000,000 Eigenvector: The Linear Algebra behind Google., Kurt Bryan, Tanya Leise, SIAM Review Vol. 48, No. 3, 2006.
2. Link Analysis: Hubs and Authorities on the World Wide Web, Chris H. Q. Ding, Hongyuan Zha, Xiaofeng He, Horst D. Simon, SIAM Review 46(2), 2002.
3. A Measure of Similarity between Graph Vertices: Applications to Synonym Extraction and Web Searching, V. D. Blondel, A.í Gajardo, M. Heymans, P. Senellart, P. Van Dooren, SIAM Review 46(4), 2004.
4. Spectral relaxation for k-means clustering, H. Zha, X. He, CH. Ding. H. Simon, M. Gu, NIPS, 2001.
5. Tensor Decompositions and Applications, T. G. Kolda, B. W. Bader, SIAM Review 51(3), 2009.
6. Higher-order web link analysis using multilinear algebra, T.Kolda, B. Bader, J. Kenny, Sandia Tech Report, 2005.

Izborni predmet 1 i 2 - Regular study - Financial and Business Mathematics

Izborni predmet 4, 5, 6 - Regular study - Financial and Business Mathematics

Izborni predmet 4, 5, 6 - Regular study - Financial and Business Mathematics