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

M. Pesenson; I. Pesenson; B. McCollum; M. Byalsky

doi:10.1117/12.855482

19 July 2010 Shannon sampling and nonlinear dynamics on graphs for representation, regularization and visualization of complex data

M. Pesenson, I. Pesenson, B. McCollum, M. Byalsky

Author Affiliations +

Proceedings Volume 7740, Software and Cyberinfrastructure for Astronomy; 77400L (2010) https://doi.org/10.1117/12.855482
Event: SPIE Astronomical Telescopes + Instrumentation, 2010, San Diego, California, United States

Abstract

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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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, Software and Cyberinfrastructure for Astronomy, 77400L (19 July 2010); https://doi.org/10.1117/12.855482

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KEYWORDS

Data compression

Astronomy

Dimension reduction

Machine learning

Data mining

Visualization

Algorithm development

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