1. komponenta

Lecture type	Total
Lectures	45

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

COURSE AIMS AND OBJECTIVES:
This course is a follow up on the course Matrix and tensor methods in data analysis. The course objectives are:
- deepen the knowledge on the previously discussed methods by using advanced techniques of multilinear (tensor) algebra, especially in the context of large dimensional problems (curse of dimensionality);
- present modern methods of learning on nonlinear manifolds, from the theoretical background to the practical implementation of software solutions.

COURSE DESCRIPTION AND SYLLABUS:
1. Classification using tensor methods.
2. Tensor and matrix methods for face and sign recognition. Comparison.
3. Numerical computation of tensor decompositions - details of algorithm implementation
3.1. CP (Canonical Polyadic)
3.2. Tucker decomposition
3.3. Tensor-Train (TT) decomposition
4. CP decomposition and HITS algorithm
5. Clustering on nonlinear structures
5.1. Diffusion distance and diffusion kernel; connection with Markov chains
5.2. Diffusion maps in applications
6. Locally linear embeddings
6.1. Idea of metric embeddings
6.2. Practical aspects (lifting trick; kernel trick)
6.3. Nystroem kernel approximation
7. Case studies (e.g. contructing a neural networks with aplpications)

1. Tensor-Train decomposition, I. Oseledets, SIAM J. Sci. Comput. Vol. 33, No. 5, pp, 2011.
2. Tensor-Train decomposition for image recognition, D. Brandoni, V. Simoncini, HAL-02196526, 2019.
3. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems, B. Nadler, S. Lafon, R. R, Coifman, I. G. Kevrekidis, Appl. Comput. Harmonic Analysis 21, 2006.
4. Matrix Methods in Data Mining and Pattern Recognition, Lars Elden, SIAM, 2007.
5. Handwritten digit classification using higher order singular value decomposition, B. Savas, L. Elden, Pattern Recognition 40(3), 2007.
6. Diffusion maps, R. R. Coifman, S. Lafon, Appl. Comput. Harmonic Analysis 21, 2006.

Enrollment :
Attended : Matrix and tensor methods in data analysis

Examination :
Passed : Matrix and tensor methods in data analysis

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics