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Dimensions of metric spaces

  • Université de Lille

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Subsets of ℝn may have “intrinsic” dimensions that are much lower than n. Consider, for example, two distinct vectors a, b ∈ ℝn and the line L = {a + tb | ∈ ℝ}. Intuitively, L has the intrinsic dimensionality 1; however, L is embedded in ℝn and from this point of view is an n-dimensional object. In this chapter we examine formalisms that lead to the definition of this intrinsic dimensionality.

Original languageEnglish
Title of host publicationAdvanced Information and Knowledge Processing
PublisherSpringer London
Pages727-766
Number of pages40
Edition9781447164067
DOIs
StatePublished - 2014

Publication series

NameAdvanced Information and Knowledge Processing
Number9781447164067
ISSN (Print)1610-3947
ISSN (Electronic)2197-8441

ASJC Scopus Subject Areas

  • Management Information Systems
  • Information Systems
  • Information Systems and Management
  • Artificial Intelligence

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