Embeddings of surfaces, curves, and moving points in euclidean space

Pankaj K. Agarwal, Sariel Har-Peled, And Hai Yu

Research output: Contribution to journalArticle

Abstract

In this paper we show that dimensionality reduction (i.e., Johnson-Lindenstrauss lemma) preserves not only the distances between static points, but also between moving points, and more generally between low-dimensional flats, polynomial curves, curves with low winding degree, and polynomial surfaces. We also show that surfaces with bounded doubling dimension can be embedded into low dimension with small additive error. Finally, we show that for points with polynomial motion, the radius of the smallest enclosing ball can be preserved under dimensionality reduction.

Original languageEnglish (US)
Pages (from-to)442-458
Number of pages17
JournalSIAM Journal on Computing
Volume42
Issue number2
DOIs
StatePublished - 2013

Keywords

  • Dimensionality reduction
  • Embeddings
  • Moving points
  • Random projection

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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