Topological and geometric tools have recently shown to be highly fruitful in data analysis and machine learning, particularly thanks to persistent homology, which has been widely studied over the last years by both theorists and practitioners. Despite its use in a huge variety of domains, persistent homology naturally comes with limitations that lead to obstructions in the interpretation of this multi-scale invariant. In particular, the development of topological methods which are noise-robust and can be incorporated into machine learning workflows in a possibly generic way remains a key challenge in this field.
I am interested in the development and investigation of robust topological representation learning procedures to face the above-mentioned problems. This includes the construction of new feature extraction algorithms, as well as the investigation of limitations and performance of these techniques. Sampling approaches to persistence and bi-filtrations are of particular interest. Applications of these techniques focus on biomedical data problems.