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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 ..."
Abstract

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 ...
The Barycenter Heuristic and the Reorderable Matrix
, 2005
"... this paper is to discuss the role of the barycenter heuristic in ordering the rows and columns of the matrix. So far, the barycenter heuristic has been mainly used in graph drawing algorithms. In order to gain full advantage of the barycenter heuristic in ordering rows and columns of the reorderable ..."
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Cited by 3 (0 self)
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this paper is to discuss the role of the barycenter heuristic in ordering the rows and columns of the matrix. So far, the barycenter heuristic has been mainly used in graph drawing algorithms. In order to gain full advantage of the barycenter heuristic in ordering rows and columns of the reorderable matrix, we survey its use in various contexts and recall the theoretical results obtained