Lectures on Clustering

These lectures give an introduction to data clustering: we discuss a few algorithms, but also look at theoretical questions related to clustering. \\**The first two lectures** are devoted to spectral clustering: graph Laplacians and their properties, spectral clustering algorithms, mathematical derivations of the algorithms, and some implementation issues. Moreover, we discuss the related modularity approach for detecting communities in networks. \\**The third lecture** is devoted to the very general question "what clustering is". We try to look at clustering from different angles, discuss different definitions of clustering, and look into theoretical foundations of clustering in general. \\**In the last lecture** we work on the question how the number of clusters should be defined. The focus is on two popular approaches: the gap statistics and the stability approach.