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

* Vector and matrix norms (including sparsity promoting)

* Mathematical foundations and algorithms for:

• Eigenvalues, SVD, pseudoinverse

• Linear regression and Least squares, also iterative solution

* Reduction and low rank representations:

• Principal Component Analysis (PCA)
• Sparse representation with l_0-norm: Orthogonal matching pursuit
• CUR factorization
• Nonnegative matrix factorization

* Applications in Data Science

• Matrix completion problems
• Dictionary learning

* Tensor computation

• Dealing with tensors and various representations: CPD, Tucker, TT
• HOSVD, Tensor OMP

* Elements of randomized numerical linear algebra:

• Randomized Range Finder and Randomized SVD
• Oblivious subspace embeddings
• The sketch-and-solve paradigm

Readings/Bibliography

Slides and material posted on Virtuale.

Teaching methods

Frontal lectures and lab sessions.

Assessment methods

Final take home project with slides presentation and oral discussion on the course material.

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

Lab facilities.

Office hours

See the website of Davide Palitta