Local embeddings of metric spaces

Ittai Abraham; Yair Bartal; Ofer Neiman

doi:10.1145/1250790.1250883

Local embeddings of metric spaces

Ittai Abraham^*, Yair Bartal, Ofer Neiman

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

16 Scopus citations

Abstract

In many application areas, complex data sets are often representedby some metric space and metric embedding is used to provide a more structured representation of the data. In many of these applications much greater emphasis is put on the preserving the local structure of the original space than on maintaining its complete structure. This is also the case in some networking applications where "small world" phenomena in communication patterns has been observed. Practical study of embedding has indeed involved with finding embeddings with this property. In this paper we initiate thestudy of local embeddings of metric spaces and provide embeddings with distortion depending solely on the local structureof the space.

Original language	English
Title of host publication	STOC'07
Subtitle of host publication	Proceedings of the 39th Annual ACM Symposium on Theory of Computing
Pages	631-640
Number of pages	10
DOIs	https://doi.org/10.1145/1250790.1250883
State	Published - 2007
Event	STOC'07: 39th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: 11 Jun 2007 → 13 Jun 2007

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	STOC'07: 39th Annual ACM Symposium on Theory of Computing
Country/Territory	United States
City	San Diego, CA
Period	11/06/07 → 13/06/07

Keywords

Metric embedding

Access to Document

10.1145/1250790.1250883

Cite this

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title = "Local embeddings of metric spaces",

abstract = "In many application areas, complex data sets are often representedby some metric space and metric embedding is used to provide a more structured representation of the data. In many of these applications much greater emphasis is put on the preserving the local structure of the original space than on maintaining its complete structure. This is also the case in some networking applications where {"}small world{"} phenomena in communication patterns has been observed. Practical study of embedding has indeed involved with finding embeddings with this property. In this paper we initiate thestudy of local embeddings of metric spaces and provide embeddings with distortion depending solely on the local structureof the space.",

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author = "Ittai Abraham and Yair Bartal and Ofer Neiman",

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language = "אנגלית",

isbn = "1595936319",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

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Abraham, I, Bartal, Y & Neiman, O 2007, Local embeddings of metric spaces. in STOC'07: Proceedings of the 39th Annual ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 631-640, STOC'07: 39th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 11/06/07. https://doi.org/10.1145/1250790.1250883

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AB - In many application areas, complex data sets are often representedby some metric space and metric embedding is used to provide a more structured representation of the data. In many of these applications much greater emphasis is put on the preserving the local structure of the original space than on maintaining its complete structure. This is also the case in some networking applications where "small world" phenomena in communication patterns has been observed. Practical study of embedding has indeed involved with finding embeddings with this property. In this paper we initiate thestudy of local embeddings of metric spaces and provide embeddings with distortion depending solely on the local structureof the space.

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T2 - STOC'07: 39th Annual ACM Symposium on Theory of Computing

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Local embeddings of metric spaces

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Keywords

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