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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.
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 ..."
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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 ...
Directed binary hierarchies and directed ultrametrics
 First joint meeting of the Société Francophone de Classification and the Classification and Data Analysis group of the Italian Statistical Society
, 2008
"... apport de recherche ISSN 02496399 ISRN INRIA/RR6815FR+ENGDirected binary hierarchies and directed ultrametrics. ..."
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apport de recherche ISSN 02496399 ISRN INRIA/RR6815FR+ENGDirected binary hierarchies and directed ultrametrics.
Comparison of interestingness measures applied to textual taxonomies matching
"... This paper presents an experimental comparison of Interestingness Measures (IMs), in the context of an approach designed for matching textual taxonomies. This extensional and asymmetric approach makes use of association rule model for matching entities issued from two textual hierarchies. We select ..."
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This paper presents an experimental comparison of Interestingness Measures (IMs), in the context of an approach designed for matching textual taxonomies. This extensional and asymmetric approach makes use of association rule model for matching entities issued from two textual hierarchies. We select 6 IMs and we perform two experiments on a benchmark composed of two textual taxonomies and a set of reference matching relations between the concepts of the two structures. The first test concerns a comparison of matching accuracy with each of the selected measures. In the second experiment, we compare how each IM evaluates reference relations by studying their values distributions. Results show that the implication intensity delivers the best results.
Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy
"... Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. “Structure ” has long been understood as s ..."
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Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. “Structure ” has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Beginning with the role of number theory in expressing data, we show how we can naturally proceed to hierarchical structures. We show how this both encapsulates traditional paradigms in data analysis, and also opens up new perspectives towards issues that are on the order of the day, including data mining of massive, high dimensional, heterogeneous data sets. Linkages with other fields are also discussed including computational logic and symbolic dynamics.
Une Nouvelle Famille d'Indices de Dissimilarite Pour la MDS
, 1993
"... : Multidimensionnal scaling ( MDS ) seeks to build points in a metric space from a given proximity data. MDS analyses the proximity data in a way that displays the structure of the distancelike data as a geometrical picture. In this paper, we study the multidimensional scaling algorithm based on in ..."
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: Multidimensionnal scaling ( MDS ) seeks to build points in a metric space from a given proximity data. MDS analyses the proximity data in a way that displays the structure of the distancelike data as a geometrical picture. In this paper, we study the multidimensional scaling algorithm based on individual differences scaling and present two new ideas for transforming scales of dissimilarities. On the other hand and mainly, we evaluate a new family of dissimilarities based on a probabilistic approach through three data sets, and compare final configurations to the the results obtained with other types of dissimilarities. Keywords: Multidimentionnal scaling ( MDS ), individual differences scaling, probabilistic approach, transforming. (Resume : tsvp) Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universit e de Rennes 1  Insa de Rennes et en Automatique  unit e de recherche de Rennes An Evalution of a New Dissimilarities Fam...
Association Rule Interestingness Measures: Experimental and Theoretical Studies
"... Summary. It is a common problem that Kdd processes may generate a large number of patterns depending on the algorithm used, and its parameters. It is hence impossible for an expert to assess these patterns. This is the case with the wellknown Apriori algorithm. One of the methods used to cope with ..."
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Summary. It is a common problem that Kdd processes may generate a large number of patterns depending on the algorithm used, and its parameters. It is hence impossible for an expert to assess these patterns. This is the case with the wellknown Apriori algorithm. One of the methods used to cope with such an amount of output depends on using association rule interestingness measures. Stating that selecting interesting rules also means using an adapted measure, we present a formal and an experimental study of 20 measures. The experimental studies carried out on 10 data sets lead to an experimental classification of the measures. This study is compared to an analysis of the formal and meaningful properties of the measures. Finally, the properties are used in a multicriteria decision analysis in order to select amongst the available measures the one or those that best take into account the user’s needs. These approaches seem to be complementary and could be useful in solving the problem of a user’s choice of measure. Key words: association rule, interestingness measure, interestingness criteria, measure classification, measure selection.
Semanticsbased classification of rule interestingness measures
"... Assessing rules with interestingness measures is the cornerstone of successful applications of association rule discovery. However, as numerous measures may be found in the literature, choosing the measures to be applied for a given application is a difficult task. In this chapter, we present a nove ..."
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Assessing rules with interestingness measures is the cornerstone of successful applications of association rule discovery. However, as numerous measures may be found in the literature, choosing the measures to be applied for a given application is a difficult task. In this chapter, we present a novel and useful classification of interestingness measures according to three criteria: the subject, the scope, and the nature of the measure. These criteria seem to us essential to grasp the meaning of the measures, and therefore to help the user to choose the ones (s)he wants to apply. Moreover, the classification allows one to compare the rules to closely related concepts such as similarities, implications, and equivalences. Finally, the classification shows that some interesting combinations of the criteria are not satisfied by any index.