Clustering Based on Wavelet Transform: Applications to Point Pattern Clustering and to High-Dimensional Data Analysis
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.
KeywordsCluster Analysis Wavelet Transform Multiresolution Analysis
Unable to display preview. Download preview PDF.
- 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.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.Murtagh, F. (1985). Multidimensional Clustering Algorithms, Physica- Verlag, Würzburg.Google Scholar
- 4.Murtagh, F. (1998). Wedding the wavelet transform and multivariate data analysis, Journal of Classification, in press.Google Scholar
- 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.Murtagh, F. and Starck, J.-L. (1998). Pattern clustering based on noise modeling in wavelet space, Pattern Recognition, in press.Google Scholar
- 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
- 10.Starck, J.-L., Murtagh, F. and Bijaoui, A. (1998). Image and Data Analysis: the Multiscale Approach, Cambridge University Press, in press.Google Scholar