97267 - Matrix Tensor Techniques for Data Science

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

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.

Readings/Bibliography

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.

Teaching methods

Blackboard, slides and computer lab sessions.

Assessment methods

Oral presentation of a takehome project (with slides)

Teaching tools

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





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Office hours

See the website of Valeria Simoncini

See the website of Margherita Porcelli