We use a redundant wavelet transform analysis to detect clusters in high-dimensional data spaces. We overcome Bellman's \curse of dimensionality" in such problems by (i) using some canonical ordering of observation and variable (document and term) dimensions in our data, (ii) applying a wavelet transform to such canonically ordered data, (iii) modeling the noise in wavelet space, (iv) dening signicant component parts of the data as opposed to insignicant or noisy component parts, and (v) reading o the resultant clusters. The overall complexity of this innovative approach is linear in the data dimensionality. We describe a number of examples and test cases, including the clustering of high-dimensional hypertext data. 1 Introduction Bellman's (1961) [1] \curse of dimensionality" refers to the exponential growth of hypervolume as a function of dimensionality. All problems become tougher as the dimensionality increases. Nowhere is this more evident than in problems related to ...

Multiscale entropy is based on the wavelet transform and noise modeling. It is a means of measuring information in a data set, which takes into account important properties of the data which are related to content. We describe in this paper how it can be used for signal and image filtering and deconvolution. We then proceed to the use of multiscale entropy for description of image content. We pursue two directions of enquiry: determining whether signal is present in the image or not, possibly at or below the image's noise level; and how multiscale entropy is very well correlated with the image's content in the case of astronomical stellar elds. Knowing that multiscale entropy represents well the content of the image, we finally use it to de ne the optimal compression rate of the image. In all cases, a range of examples illustrate these new results.

We compare dierent strategies for data ltering in wavelet space. Filtering strategy concerns both the wavelet transform algorithm used, and the processing carried out on the wavelet coecients. We present and analyze the results obtained from a set of around two hundred ltered images. Then we show that the combination of dierent ltering methods improves the quality of the ltering. 1 1 Introduction Observed data Y in the physical sciences are generally corrupted by noise, which is often additive and which follows in many cases a Gaussian distribution, a Poisson distribution, or a combination of both. Many methods have been developed during this century in order to remove the corrupted part of the signal. Each class of methods consists of considering a vision model, and using this a priori knowledge to make some assumptions about the noise in order to remove it. For instance, Fourier based ltering methods (e.g. Wiener ltering) apodizes certain frequencies where the signal-to-no...