Spectral Clustering: a Tutorial for the 2010’s

Spectral clustering is a family of methods to find K clusters using the eigenvectors of a matrix. Typically, this matrix is derived from a set of pairwise similarities Sij between the points to be clustered. This task is called similarity based clustering, graph clustering, or clustering of diadic data. One remarkable advantage of spectral clustering is its ability to cluster “points” which are not necessarily vectors, and to use for this a“similarity”, which is less restrictive than a distance. A second advantage of spectral clustering is its flexibility; it can find clusters of arbitrary shapes, under realistic separations. This chapter introduces the similarity based clustering paradigm, describes the algorithms used, and sets the foundations for understanding these algorithms. Practical aspects, such as obtaining the similarities are also discussed. ∗This tutorial appeared in “Handbook of Cluster ANalysis” by Christian Hennig, Marina Meila, Fionn Murthagh and Roberto Rocci (eds.), CRC Press, 2015.