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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2245))


We propose a novel approach to clustering, based on deterministic analysis of random walks on the weighted graph associated with the clustering problem. The method is centered around what we shall call separating operators, which are applied repeatedly to sharpen the distinction between the weights of inter-cluster edges (the so-called separators), and those of intra-cluster edges. These operators can be used as a stand-alone for some problems, but become particularly powerful when embedded in a classical multi-scale framework and/or enhanced by other known techniques, such as agglomerative clustering. The resulting algorithms are simple, fast and general, and appear to have many useful applications.

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  1. V. Estivill-Castro and I. Lee,“AUTOCLUST: Automatic Clustering via Boundary Extraction for Mining Massive Point-Data Sets”, 5th International Conference on Geocomputation, GeoComputation CD-ROM: GC049, ISBN 0-9533477-2-9.

    Google Scholar 

  2. Y. Gdalyahu, D. Weinshall and M. Werman, “Stochastic Image Segmentation by Typical Cuts”, Proceedings IEEE Conference on Computer Vision and Pattern Recognition, 1999, pp. 588–601.

    Google Scholar 

  3. S. Guha, R. Rastogi and K. Shim, “ROCK: A Robust Clustering Algorithm for Categorical Attributes”, Proceedings of the 15th International Conference on Data Engineering, pp. 512–521, 1999.

    Google Scholar 

  4. L. Hagen and A. Kahng, “A New Approach to Effective Circuit Clustering”, Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, pp. 422–427, 1992.

    Google Scholar 

  5. D. Harel and Y. Koren, “Clustering Spatial Data using Random Walks”, Proc.7th ACM SIGKDD Int.Conf.on Knowledge Discovery and Data Mining (KDD-2001), ACM, pp. 281–286, 2000.

    Google Scholar 

  6. D. Harel and Y. Koren, “Clustering Spatial Data Using Random Walks”, Technical Report MCS01-08, Dept. of Computer Science and Applied Mathematics, The Weizmann Institute of Science, 2001. Available at:

  7. A. K. Jain and R. C. Dubes, Algorithms for Clustering Data, Prentice Hall, Englewood Cliffs, New Jersy, 1988.

    MATH  Google Scholar 

  8. A. K. Jain, M.N. Murty and P.J. Flynn, “Data Clustering: A Review”, ACM Computing Surveys, 31 (1999), 264–323.

    Article  Google Scholar 

  9. G. Karypis, E. Han, and V. Kumar, “CHAMELEON: A Hierarchical Clustering Algorithm Using Dynamic Modeling”, IEEE Computer, 32 (1999), 68–75.

    Google Scholar 

  10. G. Karypis and V. Kumar, “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs”, SIAM Journal on Scientific Computing 20:1 (1999), 359–392.

    Article  MATH  MathSciNet  Google Scholar 

  11. E. Sharon, A. Brandt and R. Basri, “Fast Multiscale Image Segmentation”, Proceedings IEEE Conference on Computer Vision and Pattern Recognition, pp. 70–77, 2000.

    Google Scholar 

  12. B. Stein and O. Niggemann, “On the Nature of Structure and its Identification”, Proceedings 25th Workshop on Graph-Theoretic Concepts in Computer Science, LNCS 1665, pp. 122–134, Springer Verlag, 1999.

    Google Scholar 

  13. N. Tishby and N. Slonim, “Data Clustering by Markovian relaxation and the Information Bottleneck Method”, Advances in Neural Information Processing Systems 13, 2000.

    Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Harel, D., Koren, Y. (2001). On Clustering Using Random Walks. In: Hariharan, R., Vinay, V., Mukund, M. (eds) FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2001. Lecture Notes in Computer Science, vol 2245. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43002-5

  • Online ISBN: 978-3-540-45294-2

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