After successful completion of the module students will be able to understand and apply the basic notions, concepts, and methods of computational linear algebra, convex optimization and differential geometry used for data analysis. In particular, they will master the use of singular value decomposition method as well as random matrices for low dimensional data representations, including fundamentals of sparse recovery problems, as e.g., compressed sensing, low rank matrix recovery, and dictionary learning algorithms. The students will be also able to manage the representation of data as clusters around manifolds in high dimensions and in random graphs, acquiring methods to construct local charts and clusters for the data. In complementary laboratory sessions they will get acquainted with suitable programming tools and environment in order to analyse relevant case studies.
- Computational linear algebra: SVD, Random matrices for low dimensional data, sparse recovery (compressed sensing, low rank matrix recovery, dictionary learning).
- Convex optimization (Stochastic gradient, ).
- Geometry of data analysis (ISOMAP, diffusion map, random graphs)
|Stephane Mallat||A Wavelet Tour of Signal Processing (Edizione 2)||Academic Press||1999||9780124666061|
|Avrim Blum, John Hopcroft, Ravi Kannan,||Foundations of Data Science||Cambridge University Press||2020|
|John A. Lee, Michel Verleysen||Nonlinear Dimensionality Reduction||Springer||2006|
|I.T. Jolliffe||Principal Component Analysis||Springer||2002|
The exam consists of written questions/exercises + oral examination. The development of a project is encouraged (but not mandatory) as an integration of the oral examination.
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