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

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Author

MF Mokbel, WG Aref, A Grama

Entry type

article

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 multidimensional space into points that are nearby in the one-dimensional space. 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 multidimensional space. We give a mathematical proof for the optimality of Spectral LPM, and also demonstrate its practical use.

Date

2003 – 03

Journal

Data Engineering, 2003. Proceedings. 19th International Conference on

Key alpha

Aref

Pages

699- 701

Publication Date

2003-03-00

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@Article{ Aref,
	title = "Spectral LPM: an optimal locality-preserving mapping using the spectral (not fractal) order",
	author = "MF Mokbel, WG Aref, A Grama",
	year = "2003",
	month = "03",
	journal = "Data Engineering, 2003. Proceedings. 19th International Conference on",
	pages = "699- 701",
	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 multidimensional space into points that are nearby in the one-dimensional space. 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 multidimensional space. We give a mathematical proof for the optimality of Spectral LPM, and also demonstrate its practical use.",
}