Multi-layer Topology Preserving Mapping for K-Means Clustering

  • Ying Wu
  • Thomas K. Doyle
  • Colin Fyfe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6936)


In this paper, we investigate the multi-layer topology preserving mapping for K-means. We present a Multi-layer Topology Preserving Mapping (MTPM) based on the idea of deep architectures. We demonstrate that the MTPM output can be used to discover the number of clusters for K-means and initialize the prototypes of K-means more reasonably. Also, K-means clusters the data based on the discovered underlying structure of the data by the MTPM. The standard wine data set is used to test our algorithm. We finally analyse a real biological data set with no prior clustering information available.


Latent Space Latent Point Quantization Error High Layer Cross Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bengio, Y., Lamblin, P., Popovici, D., Larochelle, H.: Greedy layer-wise training of deep networks. In: Advances in Neural Information Processing Systems, vol. 19, pp. 153–160. MIT Press, Cambridge (2007)Google Scholar
  2. 2.
    Bengio, Y., LeCun, Y.: Large-Scale Kernel Machines. In: Scaling Learning Algorithms towards AI. MIT Press, Cambridge (2007)Google Scholar
  3. 3.
    Bishop, C.M., Svensen, M., Williams, C.K.I.: GTM: The generative topographic mapping. Neural Computation 10, 215–234 (1998)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bottou, L., Bengio, Y.: Convergence properties of the k-means algorithms. In: Advances in Neural Information Processing Systems, vol. 7, pp. 585–592. MIT Press, Cambridge (1995)Google Scholar
  5. 5.
    de Boer, P.-T., Kroese, D.P., Mannor, S., Rubenstein, R.Y.: A tutorial on the cross-entropy method. Annals of Operations Research 134(1), 19–67 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Doyle, T.K., Houghton, J.D.R., O’Suilleabhain, P.F., Hobson, V.J., Marnell, F., Davenport, J., Hays, G.C.: Leatherback turtles satellite tagged in european waters. Endangered Species Research 4, 23–31 (2008)CrossRefGoogle Scholar
  7. 7.
    Fedak, M., Lovell, P., McConnell, B., Hunter, C.: Overcoming the constraints of long range radio telemetry from animals: Getting more useful data from smaller packages. Integrative and Comparative Biology 42(1), 3–10 (2002)CrossRefGoogle Scholar
  8. 8.
    Fyfe, C.: Two topographic maps for data visualization. Data Mining and Kownledge Discovery 14, 207–224 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hays, G.C., Houghton, J.D.R., Isaacs, C., King, R.S., Lloyd, C., Lovell, P.: First records of oceanic dive profiles for leatherback turtles, dermochelys coriacea, indicate behavioural plasticity associated with long-distance migration. Animal Behaviour 67(4), 733–743 (2004)CrossRefGoogle Scholar
  10. 10.
    Hinton, G.E.: Training products of experts by minimizing contrastive divergence. Technical Report 2000-004, Gatsby Computational Neuroscience Unit. University College, London (2000)Google Scholar
  11. 11.
    Hinton, G.E., Osindero, S., Teh, Y.: A fast learning algorithm for deep belief nets. Neural Computation 16, 1527–1554 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Hinton, G.E., Salakhutdinov, R.R.: Reducing the demensionality of data with neural networks. Science 313, 504–507 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kohonen, T.: Self-organising maps. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  14. 14.
    MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Le Cam, L.M., Neyman, J. (eds.) Proc. of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press, Berkeley (1967)Google Scholar
  15. 15.
    Rubinstein, R.Y.: Optimization of computer simulation models with rare events. European Journal of Operations Reasearch 99, 89–112 (1997)CrossRefGoogle Scholar
  16. 16.
    Wu, Y., Fyfe, C.: The on-line cross entropy method for unsupervised data exploration. WSEAS Transactions on Mathematics 6(12), 865–877 (2007)MathSciNetGoogle Scholar
  17. 17.
    Wu, Y., Fyfe, C.: Topology preserving mappings using cross entropy adaptation. In: International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ying Wu
    • 1
  • Thomas K. Doyle
    • 1
  • Colin Fyfe
    • 2
  1. 1.Coastal and Marine Research Centre, ERIUniversity College Cork Glucksman Marine FacilityHaulbowlineIreland
  2. 2.Applied Computational Intelligence Research UnitThe University of the West of ScotlandScotland

Personalised recommendations