PhD Courses in Denmark

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.

For additional information, updates, and registration, please refer to AAU PhD Moodle via the link provided on the right side of this page.