Clustering Based on Wavelet Transform: Applications to Point Pattern Clustering and to High-Dimensional Data Analysis

  • F. Murtagh
  • J. L. Starck
  • M. Berry
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


We describe an effective approach to object or feature detection in point patterns via noise modeling. This is based on use of a redundant or non-pyramidal wavelet transform. Noise modeling is based on a Poisson process. We illustrate this new method with a range of examples. We use the close relationship between image (pixelated) and point representations to achieve the result of a clustering method with constant-time computational cost. We then proceed to generalize this method for high-dimensional data. Using a dataset of very well-known structure as a test case, we show proof of concept for this approach to analysis of high-dimensional boolean hyperlink datasets.


Cluster Analysis Wavelet Transform Multiresolution Analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berry, M.W., Hendrickson, B. and Raghavan, P. (1996). Sparse matrix reordering schemes for browsing hypertext, in Lectures in Applied Mathematics (LAM) Vol 32: The Mathematics of Numerical Analysis, J. Renegar, M. Shub, and S. Smale ( Eds. ), American Mathematical Society, 99–123.Google Scholar
  2. 2.
    Bijaoui, A., Starck, J.-L. and Murtagh, F. (1994). Restauration des images multi-echelles par l’gorithme a trous, Traitement du Signal, 11, 229–243.Google Scholar
  3. 3.
    Murtagh, F. (1985). Multidimensional Clustering Algorithms, Physica- Verlag, Würzburg.Google Scholar
  4. 4.
    Murtagh, F. (1998). Wedding the wavelet transform and multivariate data analysis, Journal of Classification, in press.Google Scholar
  5. 5.
    Murtagh, F., Starck, J.-L. and Bijaoui, A. (1995). Image restoration with noise suppression using a multiresolution support, Astronomy and Astrophysics Supplement Series, 112, 179–189.Google Scholar
  6. 6.
    Murtagh, F. and Starck, J.-L. (1998). Pattern clustering based on noise modeling in wavelet space, Pattern Recognition, in press.Google Scholar
  7. 7.
    Shensa, M.J. (1992). The discrete wavelet transform: wedding the a trous and Mallat lgorithms, IEEE Transactions on Signal Processing, 40, 2464–2482.CrossRefGoogle Scholar
  8. 8.
    Starck, J.-L. and Murtagh, F. (1994). Image restoration with noise suppression using the wavelet transform, Astronomy and Astrophysics, 288, 342–348.Google Scholar
  9. 9.
    Starck, J.-L., Bijaoui, A. and Murtagh, F. (1995). Multiresolution support applied to image filtering and deconvolution, Graphical Models and Image Processing, 57, 420–431.CrossRefGoogle Scholar
  10. 10.
    Starck, J.-L., Murtagh, F. and Bijaoui, A. (1998). Image and Data Analysis: the Multiscale Approach, Cambridge University Press, in press.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • F. Murtagh
    • 1
  • J. L. Starck
    • 2
  • M. Berry
    • 3
  1. 1.Faculty of InformaticsUniversity of UlsterNorthern Ireland
  2. 2.CEA/DSM/DAPNIAGif-sur-Yvette cedexFrance
  3. 3.Department of Computer ScienceUniversity of TennesseeKnoxvilleUSA

Personalised recommendations