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15
The Haar wavelet transform of a dendrogram
 Journal of Classification
, 2007
"... We consider the wavelet transform of a finite, rooted, noderanked, pway tree, focusing on the case of binary (p = 2) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how t ..."
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Cited by 16 (5 self)
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We consider the wavelet transform of a finite, rooted, noderanked, pway tree, focusing on the case of binary (p = 2) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how this works in our tree context.
Clustering in Massive Data Sets
 Handbook of massive data sets
, 1999
"... We review the time and storage costs of search and clustering algorithms. We exemplify these, based on casestudies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, ..."
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Cited by 11 (0 self)
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We review the time and storage costs of search and clustering algorithms. We exemplify these, based on casestudies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, and a basis for clustering algorithms to follow. Sections 7 to 11 review a number of families of clustering algorithm. Sections 12 to 14 relate to visual or image representations of data sets, from which a number of interesting algorithmic developments arise.
Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform
 The Computer Journal
, 2000
"... We use a redundant wavelet transform analysis to detect clusters in highdimensional 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 t ..."
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Cited by 10 (3 self)
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We use a redundant wavelet transform analysis to detect clusters in highdimensional 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 highdimensional 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 ...
Blind component separation in wavelet space: Application to CMB analysis
 EURASIP Journal on Applied Signal Processing
, 2005
"... It is a recurrent issue in astronomical data analysis that observations are incomplete maps with missing patches or intentionally masked parts. In addition, many astrophysical emissions are non stationary processes over the sky. All these effects impair data processing techniques which work in the F ..."
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Cited by 9 (4 self)
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It is a recurrent issue in astronomical data analysis that observations are incomplete maps with missing patches or intentionally masked parts. In addition, many astrophysical emissions are non stationary processes over the sky. All these effects impair data processing techniques which work in the Fourier domain. Spectral matching ICA (SMICA) is a source separation method based on spectral matching in Fourier space designed for the separation of diffuse astrophysical emissions in Cosmic Microwave Background observations. This paper proposes an extension of SMICA to the wavelet domain and demonstrates the effectiveness of waveletbased statistics for dealing with gaps in the data.
On NeuroWavelet Modeling
 The Journal of Decision Supprort System
, 2003
"... We survey a number of applications of the wavelet transform in time series prediction. ..."
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We survey a number of applications of the wavelet transform in time series prediction.
Computational Astronomy: Current Directions And Future Perspectives
"... . We review data analysis, pursuing the following lines of enquiry: traditional, numeric data analysis, based on graphical means; \active" data analysis, where the results provide new graphical user interfaces, or where the results are used to facilitate navigation in information spaces; and newly d ..."
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. We review data analysis, pursuing the following lines of enquiry: traditional, numeric data analysis, based on graphical means; \active" data analysis, where the results provide new graphical user interfaces, or where the results are used to facilitate navigation in information spaces; and newly developed tools and techniques for the processing of image and other signal objects. 1. Data Analysis for Visualization Frequently the analyst must interact with the data. This means that one type of display is made, followed by a dierent visualization of some subset of the data. The term \exploratory data analysis" is most closely associated with the name of Tukey (Princeton). Interactive statistics is another term used, and this activity may be supported by computer software. A prime example is the S language (or software environment) originating in ATT Bell Labs, and enhanced as the SPlus package by MathSoft Inc. (formerly StatSci Inc.). Figures 1, 2 and 3 illustrate complementary view...
Image Filtering by Combining Multiple Vision Models
, 1999
"... 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 th ..."
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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 signaltono...
Distributed Visual Information Management in Astronomy
, 2002
"... ometry (for example, accumulated flux data) oreffecti0HU detect miect objects. Havit brit descri.) the field'ssciOflx)0 needs, we can now look at how astronomers are expli88)0 usiR resolutix and scale toassifi data (idata tabular, and other) handliO) These new DISTRIBUTED VISUAL INFORMATION MANAGE ..."
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ometry (for example, accumulated flux data) oreffecti0HU detect miect objects. Havit brit descri.) the field'ssciOflx)0 needs, we can now look at how astronomers are expli88)0 usiR resolutix and scale toassifi data (idata tabular, and other) handliO) These new DISTRIBUTED VISUAL INFORMATION MANAGEMENT IN ASTRONOMY Resolution scale is central to largeimage visualization, offering one way to address astronomers' need to access and retrieve data. In addition, multipleresolution information and entropy are closely related to compression rate, all three of which are related to the relevance and importance of information. FIONN MURTAGH Queen'sUnivwH581 , Belfast JEANLUC STARCK French Atomic Energy Commission MIREILLE LOUYS Univ11754 Louis Pasteur 15219615/02/$17.00 2002 IEEE FEATURE A STRONOMY vantagepoiag help astronomers address the field's sciR8)0fl needs. We first look at how resolutifi and scale arei)xOOHx)0flfi iO8 sci)iHx ici compressi0fl Compressifl i tim to i) formati
Intelligent Data Modeling based on the Wavelet Transform and Data Entropy
"... . Using a small dataset resulting from a new optical engineering technique for the ngerprinting of beverages and other liquids, we develop and study an approach to quantitatively characterizing the inherent information in our data. To do this we use properties of the data which are related to resolu ..."
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. Using a small dataset resulting from a new optical engineering technique for the ngerprinting of beverages and other liquids, we develop and study an approach to quantitatively characterizing the inherent information in our data. To do this we use properties of the data which are related to resolution scale and noise. We demonstrate the eectiveness of such intelligent data modeling. 1 Introduction It has become standard to illustrate clustering and other data analysis methods using whiskies (Lapointe and Legendre, 1994; Wishart, 1998). In this paper we also use data on whiskey (Jameson) and other beverages to illustrate new approaches for taking a priori information on our data into account. The types of a priori information which we take into account include resolution scale and noise. Our goal is to develop general characterization of information content in data, to allow retrieval in unsupervised modes (data mining, clustering) or supervised modes (supervised classication, di...
Fractal and Multiscale Methods for ContentBased Image Retrieval
, 2000
"... We review recent work on a forensic science application, involving database matching of shoeprint images, using fractals. We then look at how to use features derived from multiple resolution scales, derived from a wavelet transform, in order to characterize the content of astronomical images. Th ..."
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We review recent work on a forensic science application, involving database matching of shoeprint images, using fractals. We then look at how to use features derived from multiple resolution scales, derived from a wavelet transform, in order to characterize the content of astronomical images. The features are combined in a new information measure, called multiscale entropy. Extensive validation tests are reported on, which indicate that this measure is capable of discriminating well between images on the basis of their content. 1 Fractal Coding for Feature Detection and Database Matching Approximately 30% of all burglaries provide usable shoemarks that may be recovered from the crime scene. The majority of crimes are committed by repeat oenders. References [16] provide further background on the importance of footprint matching in forensic science. We have been investigating fractals as a means of characterizing shape information in an image. A fractal is an object the over...