Given a set of points with their mutual similarities one has the task to find clusters of near or similar points and to separate dissimilar points. Spectral Clustering methods are well-known in theory and applications. They have in common that they work with Eigenvectors of matrices derived from the mutual distances or similarities of the points to be separated. As you see in the literature there is much interest in it right now. My focus of interest is an analysis of the methods, in which sense they do "good" clustering, and in which cases they work better or less good. Moreover I am interested in the connection to random walks. I have not worked on modelling issues such as finding good similarties, or implementation details like fast calculation of Eigenvectors or numerical problems. In the talk I will explain the methods, I will give sense to the term "good", I will explain the connection to random walks and I will give several random walk properties which distinguish points in different clusters.
Forschungs-