Bounding the misclassification error in spectral partitioning in the planted partition model

Abstract. A partitioning of a set of n items is a grouping of these items into k disjoint, equally sized classes. Any partition can be modeled as a graph. The items become the vertices of the graph and two vertices are connected by an edge if and only if the associated items belong to the same class. In a planted partition model a graph that models a partition is given, which is obscured by random noise, i.e., edges within a class can get removed and edges between classes can get inserted. The task is to reconstruct the planted partition from this graph. We design a spectral partitioning algorithm and analyze how many items it misclassifies in the worst case. The number of classes k is one parameter in the model that allows to control the difficulty of the problem. Our analysis extends the range of k for which any non-trivial quality guarantees can be given.