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Eigenmaps and minimal and bandlimited immersions of graphs into Euclidean spaces

Pesenson, Isaac Z. and Pesenson, Meyer Z. (2010) Eigenmaps and minimal and bandlimited immersions of graphs into Euclidean spaces. Journal of Mathematical Analysis and Applications, 366 (1). pp. 137-152. ISSN 0022-247X. http://resolver.caltech.edu/CaltechAUTHORS:20100305-142000806

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Abstract

We introduce concepts of minimal immersions and bandlimited (Paley–Wiener) immersions of combinatorial weighted graphs (finite or infinite) into Euclidean spaces. The notion of bandlimited immersions generalizes the known concept of eigenmaps of graphs. It is shown that our minimal immersions can be used to perform interpolation, smoothing and approximation of immersions of graphs into Euclidean spaces. It is proved that under certain conditions minimal immersions converge to bandlimited immersions. Explicit expressions of minimal immersions in terms of eigenmaps are given. The results can find applications for data dimension reduction, image processing, computer graphics, visualization and learning theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jmaa.2009.10.062 DOIUNSPECIFIED
Additional Information:© 2009 Elsevier Inc. Received 21 January 2009. Submitted by R.H. Torres. Available online 30 October 2009. The authors were supported in part by the National Geospatial-Intelligence Agency University Research Initiative (NURI), grant HM1582-08-1-0019.
Funders:
Funding AgencyGrant Number
National Geospatial-Intelligence Agency University Research Initiative (NURI)HM1582-08-1-0019
Subject Keywords:Combinatorial weighted graphs; Combinatorial Laplace operator; Minimal immersions into Euclidean spaces; Bandlimited immersions; Eigenmaps; Interpolation; Approximation; Reconstruction
Record Number:CaltechAUTHORS:20100305-142000806
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100305-142000806
Official Citation:Isaac Z. Pesenson, Meyer Z. Pesenson, Eigenmaps and minimal and bandlimited immersions of graphs into Euclidean spaces, Journal of Mathematical Analysis and Applications, Volume 366, Issue 1, 1 June 2010, Pages 137-152, ISSN 0022-247X, DOI: 10.1016/j.jmaa.2009.10.062. (http://www.sciencedirect.com/science/article/B6WK2-4XK45KN-3/2/9d0094bf742b33a9b48e3b0d88389c6b)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17679
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Mar 2010 19:40
Last Modified:26 Dec 2012 11:49

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