Skip to main content

Mixtures of Radial Densities for Clustering Graphs

  • Conference paper
Computer Analysis of Images and Patterns (CAIP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8047))

Included in the following conference series:

  • 2570 Accesses

Abstract

We address the problem of unsupervised learning on graphs. The contribution is twofold: (1) we propose an EM algorithm for estimating the parameters of a mixture of radial densities on graphs on the basis of the graph orbifold framework; and (2) we compare orbifold-based clustering algorithms including the proposed EM algorithm against state-of-the-art methods based on pairwise dissimilarities. The results show that orbifold-based clustering methods complement the existing arsenal of clustering methods on graphs.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)

    Article  Google Scholar 

  2. Gold, S., Rangarajan, E., Mjolsness, A.: Learning with preknowledge: clustering with point and graph matching distance measures. Neural Computation 8(4), 787–804 (1996)

    Article  Google Scholar 

  3. Günter, S., Bunke, H.: Self-organizing map for clustering in the graph domain. Pattern Recognition Letters 23(4), 405–417 (2002)

    Article  MATH  Google Scholar 

  4. Jain, B.J., Obermayer, K.: Algorithms for the Sample Mean of Graphs. In: Jiang, X., Petkov, N. (eds.) CAIP 2009. LNCS, vol. 5702, pp. 351–359. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Jain, B., Obermayer, K.: Structure spaces. The Journal of Machine Learning Research 10 (2009)

    Google Scholar 

  6. Jain, B.J., Obermayer, K.: Large sample statistics in the domain of graphs. In: Hancock, E.R., Wilson, R.C., Windeatt, T., Ulusoy, I., Escolano, F. (eds.) SSPR&SPR 2010. LNCS, vol. 6218, pp. 690–697. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Jain, B., Obermayer, K.: Maximum Likelihood Method for Parameter Estimation of Bell-Shaped Functions on Graphs. Pat. Rec. Letters 33(15), 2000–2010 (2012)

    Article  Google Scholar 

  8. Jain, B.J., Obermayer, K.: Graph quantization. Computer Vision and Image Understanding 115(7), 946–961 (2011)

    Article  Google Scholar 

  9. Jain, B.J., Wysotzki, F.: Central clustering of attributed graphs. Machine Learning 56(1), 169–207 (2004)

    Article  MATH  Google Scholar 

  10. Kaufman, L., Rousseeuw, P.: Clustering by means of medoids. Statistical Data Analysis Based on the L 1-Norm and Related Methods, 405–416 (1987)

    Google Scholar 

  11. Lozano, M.A., Escolano, F.: Protein classification by matching and clustering surface graphs. Pattern Recognition 39(4), 539–551 (2006)

    Article  MATH  Google Scholar 

  12. Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. Advances in Neural Information Processing Systems 2, 849–856 (2002)

    Google Scholar 

  13. Ng, R.T., Han, J.: Efficient and effective clustering methods for spatial data mining. In: Proceedings of the 20th International Conference on Very Large Data Bases, VLDB 1994, pp. 144–155 (1994)

    Google Scholar 

  14. Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Ward, J.H.: Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association 58(301) (1963)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jain, B.J. (2013). Mixtures of Radial Densities for Clustering Graphs. In: Wilson, R., Hancock, E., Bors, A., Smith, W. (eds) Computer Analysis of Images and Patterns. CAIP 2013. Lecture Notes in Computer Science, vol 8047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40261-6_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40261-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40260-9

  • Online ISBN: 978-3-642-40261-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics