Course detail

Welcome to Topological Signal Processing and Machine Learning: Theory and Applications

Description: 
Data with irregular and complex structures are increasingly encountered in socio-technological and natural systems, including social networks, financial markets, power and water systems, sensor networks, neuroscience, protein–protein interactions, gene regulatory networks, and molecular data. Because such data exhibit intricate relationships, they demand new signal processing and machine learning tools that account for their underlying structure, often represented as graphs or more generally as topological objects. Over the last decade, graph signal processing (GSP) and graph neural networks (GNNs) have emerged as powerful frameworks, with applications ranging from recommender systems, social networks, and misinformation detection to drug discovery, molecular property prediction, and protein folding breakthroughs such as AlphaFold. However, graphs capture only pairwise relations, whereas higher-order topological objects such as simplicial complexes and hypergraphs enable the extension of these techniques to a broader class of problems, leading to the development of topological signal processing and topological deep learning.

This course introduces the foundations and principles of topological signal processing and machine learning, with the goal of providing students with both the theoretical underpinnings and practical tools needed to analyze complex data with irregular structures. The course addresses challenges that arise in socio-technological and natural systems, where data often appear in the form of graphs, simplicial complexes, or other topological objects. Applications will be drawn from domains such as recommender systems, water networks, multivariate time series, molecular data, and neuroscience.

Topics will include:

1. Graph-based methods: graph representation learning, graph signal processing (GSP), and graph neural networks (GNNs)
2. Topological structures: simplicial complexes, hypergraphs, and higher-order interactions in data
3. Topological signal processing: fundamentals, filtering, and spectral analysis on complex topological domains
4. Topological deep learning: neural architectures for higher-order and topological data
5. Applications: case studies in social networks, critical infrastructure, molecular property prediction, and protein folding 
   

Prerequisites:

• Machine learning such as data division in train-validation-test, loss function, overfitting, and regularization;
• Basics in programming: python or equivalents, minimal experience with Pytorch / TensorFlow or equivalents is helpful but not strongly expected.

Learning Objectives:

1. Recognise key challenges in performing signal processing and machine learning with complex data
2. Compare and explain the inner working mechanisms of different methods rooted in topological signal processing and machine learning
3. Analyse different learning techniques for topological data
4. Implement guided solutions to practical applications

Organizer: Qiongxiu Li

Lecturers: Qiongxiu Li and Elvin Isufi (Associate Professor, TU Delft)

ECTS: 3

Time: 26, 27, 28 and 29 May, 2026

Place: Aalborg University

City: Copenhagen

Maximal number of participants: 50

Deadline: 05 May 2026

Important information concerning PhD courses: 

There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.

We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.

For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at phdcourses@adm.aau.dk When contacting us please state the course title and course period. Thank you.