# Graph Information Processing

**Lecturer:** Gerald Matz

**Target Audience: **MSCE and Master EI

**Language:** English

**Additional Information:** TUMonline

### Lectures/Tutorials in Summer Semester 2023

The course starts with two **on-site** lectures on **April 20** and **21** in rooms **N1090 **and** N1080,**respectively** **from **1 p.m. to 3 p.m.** each day.

Further **on-site** lectures will be offered at **May 11** and **12,** **June 15** and **16,** and **July 13 **(final lecture) in rooms **N1090 (on Thursday) **and** N1080 (on Friday)** from **1 p.m. to 3 p.m.**

All other lectures/tutorials take place on a **weekly basis via Zoom **on **Thursday **from **1 p.m. to 3 p.m.** and **Friday** from **1 p.m. to 3 p.m.**

**Further details can be found on TUMonline.**

### Content

###### COURSE DESCRIPTION

The goal of this course is to equip students with state-of-the-art know-how regarding graph-based information engineering in communications, data science, machine learning, and biomedical engineering. This comprises the use of graphs both as modelling tool for large-scale datasets and as computational paradigm for devising efficient, possibly distributed algorithms. The concepts and methods discussed in the course are applicable to problems in communication and sensor networks, infrastructure networks, social networks, traffic networks, and biological networks. After successful completion of the course, students are able to apply methods from the areas of probabilistic graphical models and graph signal processing to practical engineering problems; this comprises the problem formulation, the analytical or numerical solution, and the qualitative and quantitative performance characterization.

###### COURSE CONTENT

PART I. INTRODUCTION:

Background and Motivation, Fundamentals of Graph Theory, Fundamentals of Probability Theory

PART II. PROBABILISTIC GRAPHICAL MODELS:

Bayesian Networks, Markov Random Fields, Factor Graphs, Inference Problems, Variable Elimination, Sum-Product Algorithm, Max-Sum Algorithm, Gaussian Message Passing, Junction Tree Algorithm, Loopy Belief Propagation, Variational Methods, Parameter Learning, Topology Learning

PART III. GRAPH SIGNAL PROCESSING:

Introduction, Spectral Graph Theory, Graph Shifts, Graph Fourier Transform, Graph Filters, Graph Gradient and Divergence, Random Graph Signals, Sampling and Interpolation, Topology Identification, Clustering and Classification

PART IV. GRAPH NEURAL NETWORKS:

Network Types, Training, Inference, Applications

###### PREREQUISITES

probability and random variables, linear algebra, fundamentals of signals and systems