Boosting Spectral Partitioning by Sampling and Iteration

A partition of a set of n items is a grouping of the items into k disjoint classes of equal size. 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 the planted partition is obscured by random noise, i.e., edges within a class can get removed and edges between classes can get inserted at random. We study the task to reconstruct the planted partition from this graph whose complexity can be controlled by the number k of classes if the noise level is fixed. The best bounds on k where the classes can be reconstructed correctly almost surely are achieved by spectral algorithms. We show that a combination of random sampling and iterating the spectral approach can boost its performance in the sense that the number of classes that can be reconstructed correctly asymptotically almost surely can be as large as k...

• Type: Conference
• Year: 2005
• Where: ISAAC
• Authors: Joachim Giesen, Dieter Mitsche
• Keywords: Disjoint Classes, ISAAC 2005, Planted Partition, Planted Partition Model