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Shannon sampling and nonlinear dynamics on graphs for representation, regularization and visualization of complex data

Pesenson, M. and McCollum, B. and Pesenson, I. and Byalsky, M. (2010) Shannon sampling and nonlinear dynamics on graphs for representation, regularization and visualization of complex data. In: Software and Cyberinfrastructure for Astronomy. Proceedings of SPIE. No.7740. Society of Photo-optical Instrumentation Engineers (SPIE) , Bellingham, WA, Art. No. 77400L. ISBN 978-0-81948-230-3.

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Data is now produced faster than it can be meaningfully analyzed. Many modern data sets present unprecedented analytical challenges, not merely because of their size but by their inherent complexity and information richness. Large numbers of astronomical objects now have dozens or hundreds of useful parameters describing each one. Traditional color-color plots using a limited number of symbols and some color-coding are clearly inadequate for finding all useful correlations given such large numbers of parameters. To capitalize on the opportunities provided by these data sets one needs to be able to organize, analyze and visualize them in fundamentally new ways. The identification and extraction of useful information in multiparametric, high-dimensional data sets - data mining - is greatly facilitated by finding simpler, that is, lower-dimensional abstract mathematical representations of the data sets that are more amenable to analysis. Dimensionality reduction consists of finding a lower-dimensional representation of high-dimensional data by constructing a set of basis functions that capture patterns intrinsic to a particular state space. Traditional methods of dimension reduction and pattern recognition often fail to work well when performed upon data sets as complex as those that now confront astronomy. We present here our developments of data compression, sampling, nonlinear dimensionality reduction, and clustering, which are important steps in the analysis of large-scale, complex datasets.

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Additional Information:© 2010 SPIE. This work was carried out with funding from the National Geospatial-Intelligence Agency University Research Initiative (NURI), grant HM1582-08-1-0019, and support from NASA to the California Institute of Technology and the Jet Propulsion Laboratory.
Funding AgencyGrant Number
National Geospatial-Intelligence AgencyHM1582-08-1-0019
Subject Keywords:data mining; data compression; graph; sampling; harmonic analysis; unsupervised learning; clustering; synchronization
Series Name:Proceedings of SPIE
Issue or Number:7740
Record Number:CaltechAUTHORS:20110421-141738847
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Official Citation:M. Pesenson, I. Pesenson, B. McCollum and M. Byalsky, "Shannon sampling and nonlinear dynamics on graphs for representation, regularization and visualization of complex data", Proc. SPIE 7740, 77400L (2010); doi:10.1117/12.855482
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23415
Deposited By: Tony Diaz
Deposited On:11 May 2011 20:02
Last Modified:03 Oct 2019 02:46

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