In recent years, spectral clustering has become one of the most popular modern clustering algorithms.

It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms

traditional clustering algorithms such as the k-means algorithm. Nevertheless, on the first glance spectral clustering

looks a bit mysterious, and it is not obvious to see why it works at all and what it really does. This article is a

tutorial introduction to spectral clustering. We describe different graph Laplacians and their basic properties,

present the most common spectral clustering algorithms, and derive those algorithms from scratch by several

different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.