Exploiting Low-Dimensional Structure in Astronomical Spectra

Details Exploiting Low-Dimensional Structure in Astronomical Spectra Exploiting Low-Dimensional Structure in Astronomical Spectra

2008-07-18

arxiv.org/abs/0807.2900v1

Astrophys.J.691:32-42,2009

Astronomy and Astrophysics

Astrophysics

24 pages, 8 figures

Scientific paper

10.1088/0004-637X/691/1/32

Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work we apply a recently-developed technique, diffusion maps, to astronomical spectra for data parameterization and dimensionality reduction, and develop a robust, eigenmode-based framework for regression. We show how our framework provides a computationally efficient means by which to predict redshifts of galaxies, and thus could inform more expensive redshift estimators such as template cross-correlation. It also provides a natural means by which to identify outliers (e.g., misclassified spectra, spectra with anomalous features). We analyze 3835 SDSS spectra and show how our framework yields a more than 95% reduction in dimensionality. Finally, we show that the prediction error of the diffusion map-based regression approach is markedly smaller than that of a similar approach based on PCA, clearly demonstrating the superiority of diffusion maps over PCA for this regression task.

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