Spectral LPM

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

Mohamed Mokbel, Walid G. Aref, Ananth Grama

Research output: Contribution to conferencePaper

7 Citations (Scopus)

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
Pages699-701
Number of pages3
DOIs
Publication statusPublished - 1 Dec 2003
Externally publishedYes
EventNineteenth International Conference on Data Ingineering - Bangalore, India
Duration: 5 Mar 20038 Mar 2003

Other

OtherNineteenth International Conference on Data Ingineering
CountryIndia
CityBangalore
Period5/3/038/3/03

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Fractals

ASJC Scopus subject areas

  • Software
  • Engineering(all)
  • Engineering (miscellaneous)

Cite this

Mokbel, M., Aref, W. G., & Grama, A. (2003). Spectral LPM: An optimal locality-preserving mapping using the spectral (not fractal) order. 699-701. Paper presented at Nineteenth International Conference on Data Ingineering, Bangalore, India. https://doi.org/10.1109/ICDE.2003.1260840

Spectral LPM : An optimal locality-preserving mapping using the spectral (not fractal) order. / Mokbel, Mohamed; Aref, Walid G.; Grama, Ananth.

2003. 699-701 Paper presented at Nineteenth International Conference on Data Ingineering, Bangalore, India.

Research output: Contribution to conferencePaper

Mokbel, M, Aref, WG & Grama, A 2003, 'Spectral LPM: An optimal locality-preserving mapping using the spectral (not fractal) order' Paper presented at Nineteenth International Conference on Data Ingineering, Bangalore, India, 5/3/03 - 8/3/03, pp. 699-701. https://doi.org/10.1109/ICDE.2003.1260840
Mokbel M, Aref WG, Grama A. Spectral LPM: An optimal locality-preserving mapping using the spectral (not fractal) order. 2003. Paper presented at Nineteenth International Conference on Data Ingineering, Bangalore, India. https://doi.org/10.1109/ICDE.2003.1260840
Mokbel, Mohamed ; Aref, Walid G. ; Grama, Ananth. / Spectral LPM : An optimal locality-preserving mapping using the spectral (not fractal) order. Paper presented at Nineteenth International Conference on Data Ingineering, Bangalore, India.3 p.
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