Skip to main content
SpringerLink
Log in

Model Complexity Control in Clustering

  • Conference paper
  • First Online:
Advances in Neural Networks (WIRN 2015)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 54))

Included in the following conference series:

Abstract

This work deals with model complexity in clustering. Methods to control complexity in unsupervised learning are reviewed. A method that decouples the number of clusters from clustering model complexity is presented and its properties are discussed with the help of experiments on benchmark data sets.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)

    Google Scholar 

  2. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Norwell, MA, USA (1981)

    Book  MATH  Google Scholar 

  3. Buhmann, J., Tishby, N.: Empirical risk approximation: a statistical learning theory of data clustering. NATO ASI series. Series F Comput. Syst. Sci. 57–68 (1998)

    Google Scholar 

  4. Buhmann, J.M.: Information theoretic model validation for clustering. In: 2010 IEEE International Symposium on Information Theory Proceedings (ISIT), pp. 1398–1402. IEEE (2010)

    Google Scholar 

  5. Chung, F.R.K.: Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92). American Mathematical Society (1997)

    Google Scholar 

  6. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Series in Telecommunications and Signal Processing. Wiley, New Jersey, USA (2006)

    MATH  Google Scholar 

  7. De Silva, V., Tenenbaum, J.B.: Sparse multidimensional scaling using landmark points. Technical report, Stanford University (2004)

    Google Scholar 

  8. Eckart, C., Young, G.: The approximation of one matrix by another of lower rank. Psychometrika 1(3), 211–218 (1936)

    Article  MATH  Google Scholar 

  9. Fiedler, M.: Algebraic connectivity of graphs. Czech. Math. J. 23(2), 298–305 (1973)

    MathSciNet  MATH  Google Scholar 

  10. Fowlkes, C., Belongie, S., Chung, F., Malik, J.: Spectral grouping using the nystrom method. IEEE Trans. Pattern Anal. Mach. Intell. 26(2), 214–225 (2004)

    Article  Google Scholar 

  11. Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 193–218 (1985)

    Google Scholar 

  12. Lee, M.D.: On the complexity of additive clustering models. J. Math. Psychol. 45(1), 131–148 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, M., Vitányi, P.M.: An Introduction to Kolmogorov Complexity and Its Applications, 3rd edn. Springer, New York (2008)

    Book  MATH  Google Scholar 

  14. Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Dietterich, T.G., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems 14. MIT Press, Cambridge, MA (2002)

    Google Scholar 

  15. Rand, W.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66, 846–850 (1971)

    Article  Google Scholar 

  16. Ridella, S., Rovetta, S., Zunino, R.: Plastic algorithm for adaptive vector quantization. Neural Comput. Appl. 7(1), 37–51 (1998)

    Article  MATH  Google Scholar 

  17. Rissanen, J.: Stochastic Complexity in Statistical Inquiry, vol. 511. World Scientific Singapore (1989)

    Google Scholar 

  18. Rose, K., Gurewitz, E., Fox, G.: A deterministic annealing approach to clustering. Pattern Recogn. Lett. 11, 589–594 (1990)

    Article  MATH  Google Scholar 

  19. Rovetta, S., Masulli, F.: Online spectral clustering and the neural mechanisms of concept formation. In: Apolloni, B., Bassis, S., Esposito, A., Morabito, F. (eds.) WIRN2014—Proceedings of the 24th Italian Workshop on Neural Networks. Springer (2014)

    Google Scholar 

  20. Schwarz, G., et al.: Estimating the dimension of a model. The Ann. Stat. 6(2), 461–464 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  21. Shannon, C.E.: A mathematical theory of communication. ACM SIGMOBILE Mob. Comput. Commun. Rev. 5(1), 3–55 (2001)

    Article  MathSciNet  Google Scholar 

  22. Shepard, R.N., Arabie, P.: Additive clustering: representation of similarities as combinations of discrete overlapping properties. Psychol. Rev. 86(2), 87 (1979)

    Article  Google Scholar 

  23. Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)

    Article  Google Scholar 

  24. Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy: The Principles and Practice of Numerical Classification. W.H. Freeman, San Francisco (1973)

    MATH  Google Scholar 

  25. Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)

    MATH  Google Scholar 

  26. Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)

    Article  MathSciNet  Google Scholar 

  27. Zamir, R., Feder, M.: On lattice quantization noise. IEEE Trans. Inf. Theor. 42(4), 1152–1159 (1996)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DIBRIS – University of Genova, Via Dodecaneso 35, 16146, Genoa, Italy

    Stefano Rovetta

Authors
  1. Stefano Rovetta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefano Rovetta .

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Milano, Milano, Italy

    Simone Bassis

  2. Department of Psychology, Seconda Università di Napoli and IIASS, Caserta, Italy

    Anna Esposito

  3. Dept. of Info., Mathematics, Ele & Trans, Univ. Mediterranea of Reggio Calabria, Reggio Calabria, Italy

    Francesco Carlo Morabito

  4. Dip. Elettronica e Telecomunicazioni, Politecnico di Torino, Torino, Italy

    Eros Pasero

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Rovetta, S. (2016). Model Complexity Control in Clustering. In: Bassis, S., Esposito, A., Morabito, F., Pasero, E. (eds) Advances in Neural Networks. WIRN 2015. Smart Innovation, Systems and Technologies, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-319-33747-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-33747-0_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33746-3

  • Online ISBN: 978-3-319-33747-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation