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


Journal Article

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. Copyright 2007 ACM.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Har-Peled, S; Yu, H

Published Date

  • October 22, 2007

Published In

  • Proceedings of the Annual Symposium on Computational Geometry

Start / End Page

  • 381 - 389

Digital Object Identifier (DOI)

  • 10.1145/1247069.1247135

Citation Source

  • Scopus