Foundations of Data Analysis

What it is about

In this module you will learn mathematical methods of data analysis, in particular linear and nonlinear procedures for data dimensionality reduction as well as techniques for reconstructive restoration of structured signals. By the end you will be able to apply and assess singular value decomposition, random matrices, compressive methods and manifold-based procedures.

What you will be able to do

• Understanding of fundamental terms and methods of computational linear algebra
• Application of singular value decomposition for low-dimensional representations
• Knowledge of random matrices and their use for dimensionality reduction
• Understanding and applying sparse-recovery methods (Compressed Sensing)
• Familiarity with low-rank matrix recovery and matrix completion
• Use of optimization basics for data-analytic problems
• Recognize and apply manifold-based procedures for nonlinear dimensionality reduction
• Knowledge of dictionary learning and representation methods (bases, frames, dictionaries)

What the module consists of

• VorlesungDelivery of content through lectures, examples and discussions; motivation for independent deepening
• ÜbungProblem sheets and solutions for self-check and deepening; initially guided, later increasingly autonomous and in small groups

Teaching method

• VorlesungIntroduction of concepts, presentation through examples and discussion for motivation and deepening
• ÜbungenPractical application of lecture content, independent solving of problems for deepening and control