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.
Partly supported by the Swiss National Science Foundation under the grant “Non-linear manifold learning”.
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Giesen, J., Mitsche, D. (2005). Bounding the Misclassification Error in Spectral Partitioning in the Planted Partition Model. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_36
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DOI: https://doi.org/10.1007/11604686_36
Publisher Name: Springer, Berlin, Heidelberg
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