Random projections preserving the Hamming distance between words

Authors:
Stefano Arca;Alberto Bertoni;Giuseppe Lipori
Affiliations:
University of Milan, Department of Computer Science, Via Comelico 39/41, 20135 Milan, Italy, {arca,bertoni,lipori}@dsi.unimi.it;University of Milan, Department of Computer Science, Via Comelico 39/41, 20135 Milan, Italy, {arca,bertoni,lipori}@dsi.unimi.it;University of Milan, Department of Computer Science, Via Comelico 39/41, 20135 Milan, Italy, {arca,bertoni,lipori}@dsi.unimi.it
Venue:
Proceedings of the 2009 conference on New Directions in Neural Networks: 18th Italian Workshop on Neural Networks: WIRN 2008
Year:
2009

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Abstract

Random projections in the Euclidean space reduce the dimensionality of the data approximately preserving the distances between points. In the hypercube it holds a weaker property: random projections approximately preserve the distances within a certain range. In this note, we show an analogous result for the metric space , where Σd is the set of words of length d on alphabet Σ and dH is the Hamming distance.