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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?
A note of caution regarding distances on graphs
as author at 27th International Conference on Machine Learning (ICML), Haifa 2010,
Introduction: Presentations of Different Views on Clustering by the Workshop Organizers
as author at Clustering,
together with: Shai Ben-David, Avrim Blum,
Stability for selecting the number of clusters: literature review, questions, and ideas
as author at Workshop on Stability and Resampling Methods for Clustering, Tübingen 2007,
Lectures on Clustering
as author at PASCAL Bootcamp in Machine Learning, Vilanova 2007,
PANEL: Experiences in research, teaching, and applications of ML
as coauthor at PASCAL Bootcamp in Machine Learning, Vilanova 2007,
together with: Colin de la Higuera (coauthor), Isabelle Guyon (coauthor), José L. Balcázar (coauthor), Joaquin Quiñonero Candela (coauthor), Mark Girolami (coauthor), Mikaela Keller (coauthor),