Skip to main content
Springer Nature Link
Log in

Critical Scale for Unsupervised Cluster Discovery

  • Conference paper
Machine Learning and Data Mining in Pattern Recognition (MLDM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4571))

Abstract

This paper addresses the scale-space clustering and a validation scheme. The scale-space clustering is an unsupervised method for grouping spatial data points based on the estimation of probability density function (PDF) using a Gaussian kernel with a variable scale parameter. It has been suggested that the detected cluster, represented as a mode of the PDF, can be validated by observing the lifetime of the mode in scale space. Statistical properties of the lifetime, however, are unclear. In this paper, we propose a concept of the ‘critical scale’ and explore perspectives on handling it for the cluster validation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Parzen, E.: On the estimation of a probability density function and mode. Annals of Mathematical Statistics 33, 1065–1076 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chakravarthy, S.V., Ghosh, J.: Scale-Based Clustering Using the Radial Basis Function Network. IEEE Trans. on Neural Networks 7(5), 1250–1261 (1996)

    Article  Google Scholar 

  3. Roberts, S.J.: Parametric and non-parametric unsupervised cluster analysis. Pattern Recognition 30(2), 261–272 (1997)

    Article  Google Scholar 

  4. Nakamura, E., Kehtarnavaz, N.: Determining number of clusters and prototype locations via multi-scale clustering. Pattern Recognition Letters 19(14), 1265–1283 (1998)

    Article  MATH  Google Scholar 

  5. Hinneburg, A., Keim, D.A.: An Efficient Approach to Clustering in Large Multimedia Databases with Noise. In: Proc. 4th International Conference on Knowledge Discovery and Data Mining, pp. 58–65 (1998)

    Google Scholar 

  6. Leung, Y., Zhang, J.-S., Xu, Z.-B.: Clustering by scale-space filtering. IEEE Trans. on Pattern Analysis and Machine Intelligence 22(12), 1396–1410 (2000)

    Article  Google Scholar 

  7. Carreira-Perpiñán, M.Á., Williams, C.K.I.: On the number of modes of a Gaussian mixture. In: Griffin, L.D, Lillholm, M. (eds.) Scale Space Methods in Computer Vision. LNCS, vol. 2695, pp. 625–640. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Carreira-Perpiñán, M.Á.: Fast nonparametric clustering with Gaussian blurring mean-shift. In: ICML 2006. ACM International Conference Proceeding Series, vol. 148, pp. 153–160 (2006)

    Google Scholar 

  9. Fukunaga, K., Hostetler, L.D.: The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Trans. on Information Theory 21(1), 32–40 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cheng, Y.: Mean shift, mode seeking, and clustering. IEEE Trans. on Pattern Analysis and Machine intelligence 17(8), 790–799 (1995)

    Article  Google Scholar 

  11. Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space. IEEE Trans. on Pattern Analysis and Machine Intelligence 24(5), 603–619 (2002)

    Article  Google Scholar 

  12. Griffin, L.D., Lillholm, M.: Mode estimation using pessimistic scale space tracking. In: Griffin, L.D, Lillholm, M. (eds.) Scale Space Methods in Computer Vision. LNCS, vol. 2695, pp. 266–280. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Witkin, A.P.: Scale space filtering. In: Proc. of 8th IJCAI, pp. 1019–1022 (1983)

    Google Scholar 

  14. Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhao, N.-Y., Iijima, T.: Theory on the method of determination of view-point and field of vision during observation and measurement of figure. IEICE Japan, Trans. D (in Japanese) 68, 508–514 (1985)

    Google Scholar 

  16. Weickert, J., Ishikawa, S., Imiya, A.: Linear scale-space has first been proposed in Japan. Journal of Mathematical Imaging and Vision 10, 237–252 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. Sporring, J., Nielsen, M., Florack, L.M.J., Johansen, P. (eds.): Gaussian Scale-Space Theory. Computational Imaging and Vision Series. Kluwer, Dordrecht (1997)

    MATH  Google Scholar 

  18. Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer, Boston (1994)

    Google Scholar 

  19. Johansen, P.: On the classification of toppoints in scale space. Journal of Mathematical Imaging and Vision 4(1), 57–67 (1994)

    Article  Google Scholar 

  20. Griffin, L.D., Colchester, A.: Superficial and deep structure in linear diffusion scale space: Isophotes, critical points and separatrices. Image and Vision Computing 13(7), 543–557 (1995)

    Article  Google Scholar 

  21. Florack, L.M.J., Kuijper, A.: The topological structure of scale-space images. Journal of Mathematical Imaging and Vision 12(1), 65–79 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Kuijper, A., Florack, L.M.J., Viergever, M.A.: Scale space hierarchy. Journal of Mathematical Imaging and Vision 18(2), 169–189 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Sakai, T., Imiya, A.: Figure field analysis of linear scale-space image. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 374–385. Springer, Heidelberg (2005)

    Google Scholar 

  24. Sakai, T., Imiya, A.: Scale-space hierarchy of singularities. In: Olsen, O.F., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 181–192. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Bratley, P., Fox, B.: Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator. ACM Trans. on Mathematical Software 14(1), 88–100 (1988)

    Article  MATH  Google Scholar 

  26. Mangasarian, O.L., Setiono, R., Wolberg, W.H.: Pattern recognition via linear programming: Theory and application to medical diagnosis. In: Proc. of the Workshop on Large-Scale Numerical Optimization, pp. 22–31 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Media and Information Technology, Chiba University, Japan

    Tomoya Sakai & Atsushi Imiya

  2. Graduate School of Science and Technology, Chiba University, Japan

    Takuto Komazaki & Shiomu Hama

Authors
  1. Tomoya Sakai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Atsushi Imiya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takuto Komazaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shiomu Hama
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Petra Perner

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sakai, T., Imiya, A., Komazaki, T., Hama, S. (2007). Critical Scale for Unsupervised Cluster Discovery. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2007. Lecture Notes in Computer Science(), vol 4571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73499-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73499-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73498-7

  • Online ISBN: 978-3-540-73499-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics