Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform

Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform (2000)

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by Fionn Murtagh , Jean-luc Starck , Michael W. Berry

Venue:	The Computer Journal
Citations:	7 - 2 self

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Datum	Value	Source
TITLE	Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform	user correction - Legacy Corrections
AUTHOR NAME	Fionn Murtagh	SVM HeaderParse 0.1
AUTHOR AFFIL	School of Computer Science, The Queen's University of Belfast,	SVM HeaderParse 0.2
AUTHOR ADDR	Belfast BT7 1NN, Northern Ireland	SVM HeaderParse 0.1
AUTHOR NAME	Jean-luc Starck	SVM HeaderParse 0.1
AUTHOR AFFIL	; and	SVM HeaderParse 0.2
AUTHOR ADDR	; CEA/DSM/DAPNIA, F-91191 Gif-sur-Yvette cedex, France	SVM HeaderParse 0.1
AUTHOR NAME	Michael W. Berry	SVM HeaderParse 0.1
AUTHOR AFFIL	Ayres Hall 114, Department of Computer Science,; University of Tennessee	SVM HeaderParse 0.2
AUTHOR ADDR	TN 37996-1301	SVM HeaderParse 0.1
ABSTRACT	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 ...	user correction - Legacy Corrections
YEAR	2000	INFERENCE
VENUE	The Computer Journal	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	107--120	INFERENCE
VOLUME	43	INFERENCE
CITATIONS	28 found	ParsCit 1.0