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ICDE
2003
IEEE

Spectral LPM: An Optimal Locality-Preserving Mapping using the Spectral (not Fractal) Order

14 years 5 months ago
Spectral LPM: An Optimal Locality-Preserving Mapping using the Spectral (not Fractal) Order
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.
Mohamed F. Mokbel, Walid G. Aref, Ananth Grama
Added 01 Nov 2009
Updated 01 Nov 2009
Type Conference
Year 2003
Where ICDE
Authors Mohamed F. Mokbel, Walid G. Aref, Ananth Grama
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