Informacje o kursie

Lehrinhalte
The course covers the following topics:
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[*]Motivation, Applications
[*]Fundamentals
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[*]definition of graphs, classes of graphs, properties of graphs, signals defined over graphs
[*]Adjecency matrix, Graph Laplacian, Graph shift operator
[*]Covariance matrix, conditional dependence, precision matrix
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[*]Graph signal processing
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[*]Consensus, Diffusion
[*]Graph spectral analysis, Graph Fourier Transform
[*]Total variational norm, Graph Frequencies
[*]Bandlimited graph signals, smoothness
[*]Graph filters, Graph sampling theorem
[*]Applications
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[*]Network topology inference
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[*]Link prediction
[*]Association network inference
[*]Tomographic network topology inference
[*]Pearson product-moment correlation
[*]Causality, Partial correlation
[*]Conditional independence graph
[*]Gaussian Markov Random Fields
[*]Graphical LASSO, Graphical LASSO with Laplacian constraint
[*]Applications
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[*]Graph analysis
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[*]Subgraph identification
[*]Cliques identification
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[*]Optimization over graphs
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[*]Average consensus, diffusion, exact diffusion
[*]Gradient tracking, push-sum algorithm, etc.
[*]Applications
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[*]Graph neuronal (convolutional) network
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Literatur
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[*]Lecture notes and slides can be downloaded here:
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[*]www.nts.tu-darmstadt.de
[*]moodle
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[*]Further reading:
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[*]Petar M. Djuric, Cédric Richard, Cooperative and Graph Signal Processing, Academic Press, 2018, ISBN 9780128136775.
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Voraussetzungen
Basic knowledge in linear algebra and matrix analysis.