Exploiting low-dimensional structure in astronomical spectra

Dimension-reduction techniques can greatly improve statistical inference in astron-omy. A standard approach is to use Principal Components Analysis (PCA). In this letter we apply a recently-developed technique, diusion maps, to astronomical spectra, and develop a robust, eigenmode-based framework for regression and data parameter-ization. We show how our framework provides a computationally ecient means by which to predict redshifts of galaxies, and thus could inform more expensive redshift es-timators such as template cross-correlation. It also provides a natural means by which to identify outliers (e.g., misclassied spectra). We analyze 3846 SDSS spectra and show how our framework yields an approximately 99 % percent reduction in dimension-ality. Finally, we show that the prediction error of the diusion map-based regression approach is markedly smaller than that of a similar approach based on PCA, clearly demonstrating the superiority of diusion maps over PCA and traditional linear data reduction techniques