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 language | English (US) |
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Pages (from-to) | 442-458 |
Number of pages | 17 |
Journal | SIAM Journal on Computing |
Volume | 42 |
Issue number | 2 |
DOIs | |
State | Published - 2013 |
Keywords
- Dimensionality reduction
- Embeddings
- Moving points
- Random projection
ASJC Scopus subject areas
- Computer Science(all)
- Mathematics(all)