Spectral LPM: An optimal locality-preserving mapping using the spectral (not fractal) order

Mohamed F. Mokbel, Walid G. Aref, Ananth Grama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

For the past two decades, fractals (e.g., the Hilbert and Peano space-filling curves) have been considered the natural method for providing a locality-preserving mapping. The idea behind a locality-preserving mapping is to map points that are nearby in the multi-dimensional space into points that are nearby in the one-dimensional space. In this paper, we argue against the use of fractals in locality-preserving mapping algorithms, and present examples with experimental evidence to show why fractals produce poor locality-preserving mappings. In addition, we propose an optimal locality-preserving mapping algorithm, termed the Spectral Locality-Preserving Mapping algorithm (Spectral LPM, for short), that makes use of the spectrum of the multi-dimensional space. We give a mathematical proof for the optimality of Spectral LPM, and also demonstrate its practical use.

Original languageEnglish (US)
Title of host publicationProceedings - International Conference on Data Engineering
EditorsU. Dayal, K. Ramamritham, T.M. Vijayaraman
Pages699-701
Number of pages3
DOIs
StatePublished - Dec 1 2003
EventNineteenth International Conference on Data Ingineering - Bangalore, India
Duration: Mar 5 2003Mar 8 2003

Other

OtherNineteenth International Conference on Data Ingineering
CountryIndia
CityBangalore
Period3/5/033/8/03

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