Exploiting Low-Dimensional Structure in Astronomical Spectra

TL;DR

This paper introduces a diffusion map-based framework for analyzing astronomical spectra, significantly reducing dimensionality and improving redshift prediction accuracy compared to PCA, while also identifying outliers effectively.

Contribution

The work applies diffusion maps to astronomical spectra, providing a more efficient and accurate regression method for redshift prediction and outlier detection than traditional PCA-based approaches.

Findings

Over 95% reduction in spectral data dimensionality

Diffusion map regression outperforms PCA in prediction accuracy

Framework effectively identifies spectral outliers

Abstract

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.