Selected Topics in ASC (STASC)5 ECTS
(englische Bezeichnung: Selected Topics in ASC)
(Prüfungsordnungsmodul: Selected Topics in ASC)
Modulverantwortliche/r: Ralf Müller
Lehrende:
Antonia Maria Tulino
| Startsemester: |
WS 2020/2021 | Dauer: |
1 Semester | Turnus: |
jährlich (WS) |
| Präsenzzeit: |
60 Std. | Eigenstudium: |
90 Std. | Sprache: |
Englisch |
Lehrveranstaltungen:
Empfohlene Voraussetzungen:
Prerequisite:
Basic knowledge of calculus, probability theory and statistics.
Inhalt:
Content:
Signal Processing over graphs
The goal of the course is to illustrate basic methodologies for graph signal processing suitable for the very
general case of signals defined over non-metric space domains, like for example in gene regulatory
networks. Graph-theoretical tools play a fundamental role in this new formulation and then they are
deeply covered during the course. Graph models are discussed and analyzed, together with operations
over graphs, like partitioning. Convex optimization is then presented and applied to several examples,
from resource allocation in communication networks to machine learning. Finally, it is shown how to
formulate and solve optimization problems in distributed form, suitable for big data applications, where
the amount of data is so big that the data cannot reside on a single machine, but are spread over a high
number of machines.
Part I:
Recap on signal properties, discrete representations, Fourier transforms, filtering, sampling
theory, applications to audio signals and images. Sparse representations, compressive sensing
Part II:
Processing over graphs.
• Algebraic graph theory, graph properties, connectivity.
• Graph features: degree centrality, eigenvector centrality, PageRank, betweeness, modularity
• Graph models: random graphs, random geometric graphs, small worlds graphs, scale-free
graphs.
• Independence graphs: Markov networks, Bayes networks, Gaussian Markov Random Fields
• Operations on graphs: partitioning.
• Signals defined on graphs
• Filtering and sampling signals over graphs.
• Prediction of processes over graphs.
• Inference of graph topology from data.
Part III:
Recap on Convex optimization: alternating direction method of multipliers, algorithms for
sparsity constrained problems-
Part IV:
Examples of application
• Graph-based methods for machine learning
• Graph topology inference from data (brain, finance, ...)
• Initial concept on. Deep Neural Network Approximation Theory
Lernziele und Kompetenzen:
The students analyze and explain recent research results presented by prominent guest professors with high international scientific reputation. The students incorporate the addressed topics and research results into their own experiences and knowledge in signal processing and communications. They use the material presented in this course in their major or minor project and/or in their Master Thesis. They develop new scientific results in the addressed research fields.
Bemerkung:
Recommended: Courses on Information Theory, Statistical Signal Processing, Digital Communications, Source and Channel Coding
Organisatorisches:
Evaluation:
There will be a few homework assignments that involve both theory and programming
components. A hard copy of your homework is required. Students are encouraged to use LaTeX
to typeset their homeworks. A final project, at the end of the course, will be also assigned. The
final evaluation will be based on the homework assignments, the project and an oral exam.
Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
- Advanced Signal Processing & Communications Engineering (Master of Science)
(Po-Vers. 2020w | TechFak | Advanced Signal Processing & Communications Engineering (Master of Science) | Gesamtkonto | Selected Topics in ASC)
Studien-/Prüfungsleistungen: