Abstract
The following probabilistic process models the generation of noisy clustering data: Clusters correspond to disjoint sets of vertices in a graph. Each two vertices from the same set are connected by an edge with probability p, and each two vertices from different sets are connected by an edge with probability r < p. The goal of the clustering problem is to reconstruct the clusters from the graph. We give algorithms that solve this problem with high probability. Compared to previous studies, our algorithms have lower time complexity and wider parameter range of applicability. In particular, our algorithms can handle O(√n/ log n) clusters in an n-vertex graph, while all previous algorithms require that the number of clusters is constant.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Ben-Dor, R. Shamir, and Z. Yakhini. Clustering gene expression patterns. J. of Computational Biology, 6:281–297, 1999.
R. B. Boppana. Eigenvalues and graph bisection: An average-case analysis. In Proc. 28th Symposium on Foundation of Computer Science (FOCS 87), pages 280–285, 1987.
T. Carson and R. Impagliazzo. Hill-climbing finds random planted bisections. In Proc. Twelfth Symposium on Discrete Algorithms (SODA 01), pages 903–909. ACM press, 2001.
H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statis., 23:493–507, 1952.
A. E. Condon and R. M. Karp. Algorithms for graph partitioning on the planted partition model. Lecture Notes in Computer Science, 1671:221–232, 1999.
M. E. Dyer and A. M. Frieze. The solution of some random NP-hard problems in polynomial expected time. J. of Algorithms, 10(4):451–489, 1989.
U. Feige and J. Kilian. Heuristics for semirandom graph problems. J. of Computer and System Sciences, To appear.
M. Jerrum and G. B. Sorkin. Simulated annealing for graph bisection. In Proc. 34th Symposium on Foundation of Computer Science (FOCS 93), pages 94–103, 1993.
A. Jules. Topics in black box optimization. PhD thesis, U. California, 1996.
V. V. Petrov. Sums of independent random variables. Springer-Verlag, 1975.
Z. Yakhini. Personal communications.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shamir, R., Tsur, D. (2002). Improved Algorithms for the Random Cluster Graph Model. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_24
Download citation
DOI: https://doi.org/10.1007/3-540-45471-3_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43866-3
Online ISBN: 978-3-540-45471-7
eBook Packages: Springer Book Archive