- Docente: Valeria Simoncini
- Credits: 6
- SSD: MAT/08
- Language: English
- Moduli: Valeria Simoncini (Modulo 1) Davide Palitta (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Sep 25, 2024 to Dec 19, 2024
Learning outcomes
At the end of the course, students have theoretical and computational knowledge on matrix and tensor techniques for analysing large amounts of data. In particular, students are able to examine large samples of discrete data and extract interpretable information of relevance in image and data processing, in medical and scientific applications, and in social and security sciences.
Course contents
* Vector and matrix norms (including sparsity promoting)
Mathematical foundations and algorithms for:
* Linear regression and Least squares
* Eigenvalues, SVD, pseudoinverse
* Reduction and low rank representation:Principal Component Analysis anf factor analysis.
- Sparse representation with l_0-norm: Orthogonal matching pursuit
- CUR factorization
-non-negative factorizations
-matrix completion
- dictionary learning
* Tensors
- Dealing with tensors and various representations
- HOSVD, Tensor OMP, Dictionary Learning with tensors
Examples with real world data.
Readings/Bibliography
Slides plus a lot of material at
http://www.dm.unibo.it/~simoncin/DataScienceLM.html
Teaching methods
Frontal lectures and lab sessions.
Assessment methods
Final take home project with slides presentation.
Oral discussion on the course material.
Teaching tools
Lab facilities
Links to further information
http://www.dm.unibo.it/~simoncin/DataScienceLM.html
Office hours
See the website of Valeria Simoncini
See the website of Davide Palitta