In a broad sense, my field of research is the theoretical analysis of machine learning algorithms. More particular, I am currently working on two major topics:

Theoretical foundations of clustering: Given that clustering is one of the most popular techniques for exploratory data analysis, it is intriguing to see how little is known about theoretical aspects of clustering. For example, for most clustering algorithms consistency statements do not exist, and we are far from being able to give performance guarantees or confidence statements on their outcomes.

My second area of interest is the combination of graph theory with machine learning and statistics. My goal is to study the statistical properties of graph based machine learning algorithms, for example in order to answer questions such as: How should we construct the similarity graphs in graph based learning algorithms? Which properties of graphs are attractive for machine learning? Which ones are misleading?