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97267 - MATRIX AND TENSOR TECHNIQUES FOR DATA SCIENCE

Anno Accademico 2021/2022

                
                        Docente:
                        Valeria Simoncini
                    
                        Crediti formativi:
                        6
                    
                        SSD:
                        MAT/08
                    
                        Lingua di insegnamento:
                        Inglese
                    
                        Moduli:
                        
                            Valeria Simoncini
                            (Modulo 1)
                        
                            Margherita Porcelli
                            (Modulo 2)
                        
                        Modalità didattica:
                        
                                    Convenzionale - Lezioni in presenza (Modulo 1)
                                
                                    Convenzionale - Lezioni in presenza (Modulo 2)
                                
                            Campus:
                            Bologna
                        
                            Corso:
                            Laurea Magistrale in
                            Matematica (cod. 5827)

                            Risorse didattiche su Virtuale

Conoscenze e abilità da conseguire

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.

Contenuti

The course presents fundamental matrix and tensor techniques commonly employed in Data Mining methods, together with optimization strategies designed to handle constrained problems typically arising in data science.

Mathematical tools will be developed for the following topics:

Clustering strategies (hierarchical, spectral, subspace-based, tec)
Compression and approximation strategies (PCA, non-negative factorizations, etc)
Dictionary learning
Matrix completion

Computational experience in Matlab/Octave on realistic data will accompany the lectures.

Testi/Bibliografia

Nocedal, Jorge, and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006.

Beck, Amir. First-order methods in optimization. Society for Industrial and Applied Mathematics, 2017.

Gillis, Nicolas. Nonnegative Matrix Factorization. SIAM, 2020.

Dumitrescu, Bogdan, and Paul Irofti. Dictionary learning algorithms and applications. Springer, 2018.

Other textbooks, recent scientific articles and case studies from real world applications will be made available during the course.

Metodi didattici

Blackboard, slides and computer lab sessions.

Modalità di verifica e valutazione dell'apprendimento

Oral presentation of a takehome project (with slides)

Strumenti a supporto della didattica

Slides made available as pdf file on the course webpage. Use of Matlab computational environment, and various toolboxes.

Orario di ricevimento

Consulta il sito web di Valeria Simoncini

Consulta il sito web di Margherita Porcelli